Light & Optics Flashcards

Always a favorite of MCAT test-makers, optical systems have become especially high-yield due to their applications to biological systems. Use these cards to master Snell’s law, diverging and converging mirrors, and combinations of lenses. For enhanced practice, think about how these concepts relate to biological systems, such as the human eye.

1
Q

What law gives the angle of reflection of a light ray from a flat surface?

A

θi = θr

This expression is the law of reflection, which states that the angle of incidence will equal the angle of reflection for a light ray striking a surface. Note that all angles are measured from the normal.

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2
Q

A light ray strikes a pane of glass, making an angle of 35º with the surface. Find the angle of reflection.

A

θr = 55º

The angle of incidence always equals the angle of reflection. However, remember that the angles of incidence and reflection must be measured relative to the normal. If the angle made with the surface is 35º, the angle made with the normal will be (90º - 35º) = 55º. θi and θr are shown below.

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3
Q

Define:

refraction

A

Refraction occurs when a light ray crosses a boundary from one transparent medium to another.

When a light ray travels between media, it will bends either toward or away from the normal, depending on the properties of the media involved.

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4
Q

Define:

index of refraction

A

The index of refraction (n) of a transparent medium is a unitless ratio of the speed of light in that medium compared to the speed of light in a vacuum.

Index of refraction is defined as n = c/v. Here, n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the medium.

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5
Q

What are the approximate indices of refraction of air, water, and glass, respectively?

A
  • nair = approximately 1
  • nwater = approximately 1.33
  • nglass varies greatly, but 1.5 is a commonly-used value on the MCAT
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6
Q

What features characterize substances with indices of refraction that are less than 1?

A

No substance has an n value that is less than 1.

Index of refraction is defined as c/v, where c is light’s speed in a vacuum and v is its speed in the relevant medium. Since light travels fastest in a vacuum, n is always equal to or greater than 1.

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7
Q

How does the path of a light ray change when it crosses a boundary from air into glass?

A

When a light ray travels from air into glass, it bends toward the normal of the surface.

Air has a lower index of refraction than glass. Whenever light moves from lower to higher index of refraction, it will angle toward the normal.

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8
Q

How does the path of a light ray change when it crosses a boundary from water into air?

A

When a light ray travels from water into air, it bends away from the normal of the surface.

Water has a higher index of refraction than air. Whenever light moves from higher to lower index of refraction, it will angle away from the normal.

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9
Q

What quantities are related by Snell’s law?

A

Snell’s law gives the relationship between the angle of incidence and that of refraction for a light ray crossing the boundary between media. The equation is:

n1sin(θ1) = n2sin(θ2)

where
n1 = index of refraction on the incident side
θ1 = angle of incidence
n2 = index of refraction on the refraction side
θ2 = angle of refraction

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10
Q

What is the critical angle (θc)?

A

The critical angle (θc) is the angle of incidence in a certain medium at which the angle of refraction into a new medium would reach 90º. Angles larger than the critical angle will result in total internal reflection.

A critical angle only exists when light is moving from a high to a low index of refraction. A classic example is refraction from diamond into air.

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11
Q

What formula is used to calculate the critical angle (θc)? Assume that light is traveling from a medium with refractive index n1 to a medium with index n2.

A

θc = sin-1(n2/n1)

This formula can be derived from Snell’s law:

n1sin(θc) = n2sin(90º)
n1sin(θc) = n2(1)
sin(θc) = n2/n1
θc = sin-1(n2/n1)

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12
Q

The utility of a fiber optic cable depends on its ability to trap light inside its own material for long distances. What property is likely involved in this example?

A

Fiber optic cables rely on total internal reflection.

In such cases, light rays stay entirely in the incident medium; no light refracts across the boundary. This only occurs if the n value of the cable is sufficiently higher than that of the outside material, and if the angle of incidence is large enough.

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13
Q

Under what conditions does total internal reflection occur?

A

For total internal reflection to occur, two conditions must be met:

  • Light must be traveling from high to low index of refraction.
  • The angle of incidence of the light ray must exceed the critical angle of the interface.
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14
Q

Define:

dispersion

A

Dispersion involves the refraction of different wavelengths of light at different angles.

The most common example of dispersion tested on the MCAT involves white light traveling through a prism. When dispersion occurs, the light splits into a spectrum of colors and spreads out at a range of angles.

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15
Q

What process causes a beam of sunlight to separate into a rainbow of colors as it passes through a prism?

A

The rainbow is produced by dispersion.

Like all white light, sunlight is made up of all the colors of visible light mixed together. Different colors of light refract differently as they pass through the prism, so they are separated upon exiting the back surface.

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16
Q

When white light is separated by a prism into its component colors, in what order do they appear?

A

The separated colors are, in order, red, orange, yellow, green, blue, indigo, violet.

This is easily remembered by the mnemonic ROYGBIV (Roy Gee Biv). Note that violet light, which travels slowly and has a high frequency, bends the most while red light bends the least.

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17
Q

Define:

focal point

A

An optic’s focal point is the location where light rays parallel to its axis will cross after reflecting from, or refracting through, the optic.

An optic with a short focal point is strong and bends light drastically, while an optic with a long focal point is weak and affects light rays less significantly.

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18
Q

In an optical system, what is an image?

A

An image is an optical reproduction of a physical object, formed when light rays transmitted by the object are converged at a specific point by an optic or series of optics.

Many optics problems will involve calculating the location of a system’s image, given a particular object and a lens or mirror.

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19
Q

What types of lens or mirror has a radius of curvature?

A

All spherical lenses and mirrors have radii of curvature.

Specifically, the radius of curvature of a mirror is the radius of the sphere from which the mirror or lens is a small portion.

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20
Q

How does the radius of curvature of a lens or mirror compare to its focal length?

A

For all spherical lenses and mirrors, the radius of curvature is equal to twice the focal length.

In other words, focal length can be found by taking one-half of the radius of curvature.

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21
Q

Lenses A and B are both converging lenses. How will the strength of the two lenses compare if the radius of curvature of Lens A is significantly larger than that of Lens B?

A

Lens B will be stronger than Lens A.

Since Lens A has a larger radius of curvature, it must also have a larger focal distance. The larger the focal length, the farther away from the lens the image will be formed; a weak lens will therefore have a large focal length. This also relates to the equation P = 1/f, which shows that power decreases as focal length increases.

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22
Q

When is the image produced by an optical system real?

A

An optical system projects a real image when light rays reflected off or transmitted through the optic cross after the reflection or transmission.

Real images include the images on movie screens and the images made by the eye on the retina.

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23
Q

When is the image produced by an optical system virtual?

A

An optical system projects a virtual image when light rays reflected off or transmitted through the optic diverging away from one another.

Virtual images include the images created by flat mirrors and magnifying glasses.

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24
Q

In what cases will a virtual image be upright, or erect?

A

Any virtual image produced by any system will be upright.

Remember “IR” and “UV”; inverted images are always real, while upright images are always virtual.

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25
Q

In what cases will a real image be upright, or erect?

A

No real image produced by a system will ever be upright. Real images are always inverted.

Remember “IR” and “UV”; inverted images are always real, while upright images are always virtual.

26
Q

What qualities define a converging mirror?

A

A mirror is converging if any inbound light ray parallel to the mirror’s principal axis crosses that axis after reflecting off the mirror.

Converging mirrors are concave in shape.

27
Q

What is the focal length of a converging mirror?

A

The focal length is the distance from the mirror to the focal point. Rays parallel to the optical axis cross at the focal point after reflecting off the mirror.

The focal length of any spherical mirror or lens is one-half of its radius of curvature.

28
Q

An optical system consists of an object and a single converging mirror. If the object is located between one and two focal lengths from the mirror, what are the properties of the final image?

A

The image is real, inverted, and magnified. It is also more distant from the mirror than the object is.

Note that converging lenses also produce real, inverted images when the object distance fits these specifications.

29
Q

An optical system consists of an object and a single converging mirror. If the object is located exactly one focal length from the mirror, what are the properties of the final image?

A

No image is formed.

Note that converging lenses also fail to produce an image when the object is positioned one focal length from the lens.

30
Q

An optical system consists of an object and a single converging mirror. If the object is located less than one focal length from the mirror, what are the properties of the final image?

A

The image is upright, virtual, and magnified. It is also more distant from the mirror than the object is.

Note that converging lenses also produce upright, virtual images when the object distance fits these specifications.

31
Q

What is the thin lens equation used to calculate?

A

The thin lens equation relates an optical system’s focal length to its object and image distance. This equation works for both lenses and mirrors.

The equation reads:

1/f = 1/o + 1/i

where
f = focal length
o = distance between optic and object
i = distance between optic and image

32
Q

What is the magnification of an optical system?

A

A optical system’s magnification is the ratio of the size of the image to the size of the object.

Magnification can be calculated from the image and object distance of the optical system. The magnification m is calculated as:

m = -(image distance/object distance)

33
Q

What does the sign of its magnification indicate about an image?

A

The sign of the magnification (positive or negative) indicates the direction that the image points.

If m > 0, the image is upright. If m < 0, the image is inverted.

34
Q

What does the magnitude of its magnification indicate about an image?

A

The magnitude of the magnification indicates the size of the image.

If |m| > 1, the image is magnified, or larger than the object. If |m| < 1, the image is reduced, or smaller than the object.

35
Q

For an optical system, the object and image distance are 30 cm and 60 cm, respectively. What is the magnification of the image?

A

m = -2

Remember, m = -i/o; so for this system:

m = -i/o = -(60/30) = -2

The image is inverted, and is twice as tall as the object.

36
Q

For an optical system, the object and image distance are 20 cm and -10 cm, respectively, What is the magnification of the image?

A

m = +½

Remember, m = -i/o; so for this system:

m = -i/o = -((-10)/20) = +½

The image is upright, and is half as tall as the object.

37
Q

What qualities define a diverging mirror?

A

A mirror is diverging if any inbound light ray which is parallel to the principal axis points away from the axis after reflecting off the mirror.

Diverging mirrors are convex in shape.

38
Q

What does the sign of an optic’s focal length indicate about its properties?

A

An optic’s focal length indicates the converging or diverging nature of the optic.

If f > 0, the optic is converging, while if f < 0, the optic is diverging. If f = infinity, the optic is planar.

39
Q

An optical system is made up of a single mirror, with an object distance of 30 cm and an image distance of -30 cm. What type is the mirror?

A

The mirror is planar. This is evident because f = infinity.

Given i and o, f can be calculated as:

1/f = 1/o + 1/i = 1/30 + 1/(-30) = 0

If 1/f = 0, f = infinity.

Planar mirrors produce virtual images, and i = -o.

40
Q

An optical system is made up of a single mirror, with an object distance of 15 cm and an image distance of 30 cm. What type is the mirror?

A

The mirror is converging, and f = 10 cm.

Given i and o, f can be calculated as:

1/f = 1/o + 1/i = 1/15 + 1/30 = 3/30
f = 30/3 = 10 cm

Only converging mirrors and lenses have positive focal lengths.

41
Q

What is the focal length of a diverging mirror?

A

The focal length is the distance from the mirror to the focal point. Virtual extensions of rays parallel to the principal axis cross at the focal point after reflecting off the mirror.

The focal length of any spherical mirror or lens is one-half of its radius of curvature.

42
Q

An optical system consists of an object and a single diverging mirror. What are the properties of the final image?

A

The image is virtual, reduced, and upright. It is also closer to the mirror than the object is.

Note that diverging lenses also always produce upright, virtual images.

43
Q

An optical system is made up of a single mirror, with an object distance of 30 cm and an image distance of -15 cm. What type is the mirror?

A

The mirror is diverging, and f = -30 cm.

Given i and o, f can be calculated as:

1/f = 1/o + 1/i = 1/30 + 1/(-15) = -1/30
f = -30 cm

A negative focal length generally correlates to a diverging system.

44
Q

What qualities define a converging lens?

A

A lens is converging if any inbound light ray which is parallel to the optical axis crosses the axis after refracting through the lens.

Converging lenses are convex in shape.

45
Q

What is the focal length of a converging lens?

A

The focal length is the distance from the lens to the focal point. Rays parallel to the principal axis cross at the focal point after refracting through the lens.

The focal length of any spherical mirror or lens is one-half of its radius of curvature.

46
Q

An optical system consists of an object and a single converging lens. If the object is located between one and two focal lengths from the lens, what are the properties of the final image?

A

The image is real, inverted, and magnified. It is also more distant from the lens than the object is.

Note that converging mirrors also produce real, inverted images when the object distance fits these specifications.

47
Q

An optical system consists of an object and a single converging lens. If the object is located exactly one focal length from the lens, what are the properties of the final image?

A

No image is formed.

Note that converging mirrors also fail to produce an image when the object is positioned one focal length from the mirror.

48
Q

An optical system consists of an object and a single converging lens. If the object is located less than one focal length from the lens, what are the properties of the final image?

A

The image is upright, virtual, and magnified. It is also more distant from the lens than the object is.

Note that converging mirrors also produce upright, virtual images when the object distance fits these specifications.

49
Q

An optical system is made up of a single lens, with an object distance of 20 cm and an image distance of 20 cm. What type is the lens?

A

The lens is converging, and f = 10 cm.

Given i and o, f can be calculated as:

1/f = 1/o + 1/i = 1/20 + 1/20 = 1/10
f = 10 cm

Only converging mirrors and lenses have positive focal lengths.

50
Q

What qualities define a diverging lens?

A

A lens is diverging if any inbound light ray which is parallel to the principal axis points away from the axis after refracting through the lens.

Diverging lenses are concave in shape.

51
Q

What is the focal length of a diverging lens?

A

The focal length is the distance from the lens to the focal point. Virtual extensions of rays parallel to the principal axis cross at the focal point after refracting through the lens.

The focal length of any spherical mirror or lens is one-half of its radius of curvature.

52
Q

An optical system consists of an object and a single diverging lens. What are the properties of the final image?

A

The image is virtual, reduced, and upright. It is also closer to the lens than the object is.

Note that diverging lenses also always produce upright, virtual images.

53
Q

An optical system is made up of a single lens, with an object distance of 45 cm and an image distance of -15 cm. What type is the lens?

A

The lens is diverging, and f = -22.5 cm.

Given i and o, f can be calculated as:

1/f = 1/o + 1/i = 1/45 + 1/(-15) = -2/45 = -1/22,5
f = -22.5 cm

A negative focal length generally correlates to a diverging system.

54
Q

What quantity is measured in diopters?

A

Diopters measure the power, or strength, of optical elements.

Power is calculated by taking the reciprocal of the focal length:

P = 1/f

Focal lengths are typically reported in m, so 1 diopter is 1 m-1. Note that you may also see optical measurements in cm.

55
Q

Which lens bends light more dramatically, a 2-diopter lens or an 8-diopter one?

A

The 8-diopter lens bends light more.

The shorter a lens’ focal length, the closer light converges on the optical axis after passing through the lens. The focal length of the 2-diopter lens is 1/2 m, while that of the 8-diopter lens is 1/8 m. The 8-diopter lens, with its shorter focal length, bends light more.

56
Q

If a 2-diopter lens is combined with a 3-diopter lens, what is the approximate strength of the combined lens system?

A

The combined lens system has a strength of approximately 5 diopters.

The diopter system is roughly additive; when multiple elements are combined, their overall diopter rating is roughly the sum of the strength of each individual element.

57
Q

Define:

chromatic aberration

A

Chromatic aberration is the characteristic colored halo around an image created by a lens.

This type of aberration occurs due to dispersion. Different colors of light will focus at different points, so an image of an object illuminated by white light will appear blurred.

58
Q

Define:

spherical aberration

A

Spherical aberration is the characteristic blurriness of an image created by a real spherical lens.

Spherical optics focus light rays well, as long as the light rays are near the center of the optic. Light rays closer to the optic’s edges, however, will not focus at exactly the same point, so images including light rays from those edges will appear blurred.

59
Q

How can the overall magnification of a multiple-lens system be calculated?

A

The overall magnification is simply the product of the magnifications of all of the individual lenses.

60
Q

The object of a two-lens optical system is 15 cm tall. If the magnifications of the lenses are m1 = +2 and m2 = +1/3, respectively, what is the overall height of the final image?

A

The final image is 10 cm tall.

The overall magnification of the system is the product of the two magnifications:

mtot = m1m2 = (2)(1/3) = 2/3

The final image is upright and 2/3 the height of the original object, or 10 cm tall.

61
Q

If a microscope has a 10x eyepiece and a 40x objective, how large will a 10 µm object appear?

A

The object will appear to measure 4 mm.

The overall magnification is (10) (40) = 400x, so the final image size is:

10 x 10-6 * 400 = 4 x 10-3 m