**Monochromatic light of a certain wavelength falls on a narrow slit. On a screen a certain distance away, the distance between the second minimum and the central maximum is 2cm. What would happen to the spacing between the two if the wavelength of the radiation were increased?**

*a) It would depend on whether the new wavelength is an odd or even multiple of the old.**b) It would remain unchanged**c) It would decrease.**d) it would increase.*

**D. It would increase.**

Electromagnetic Spectrum

__ The following units __are often used when quoting wavelengths:

- 1 mm = 10
^{− 3}m, - 1 μ m = 10
^{− 6}m, - 1 nm = 10
^{− 9}m, and - 1 Å (angstrom) = 10
^{− 10}m.

__ The full spectrum__ is broken up into many regions, which in descending order of wavelength are

- radio (10
^{9}m− 1 m), - microwave (1 m− 1 mm),
- infrared (1 mm− 700 nm),
- visible light (700 nm− 400 nm),
- ultraviolet (400 nm− 50 nm),
- x-ray (50 nm− 10− 2 nm), and
- gamma rays (less than 10− 2 nm).

electromagnetic waves

speed of light

c=3 × 10^{8 }m/s

**c=fλ**

*blackbody*

###
- used to describe an ideal radiator
- refers to the fact that such an object is also an ideal absorber and would appear totally black if it were at a lower temperature than its surroundings

rectilinear propagation

When light travels through a single homogeneous medium, it travels in a straight line

geometrical optics.

behavior of light at the boundary of a medium or interface between two media is described by this theory

law of reflection

θ_{ 1}=θ_{2}

where θ _{1} is the incident angle and θ _{2} is the reflected angle, both measured from the normal

real image

light actually converges at the position of the image

virtual image

light only appears to be coming from the position of the image but does not actually converge there.

- Because the light does not converge at all, plane mirrors always create virtual images

center of curvature (C)

a point on the optical axis located at a distance equal to the radius of curvature from the vertex of the mirror;

*in other words, where the center of the mirrored sphere would be, were it a complete sphere.*

radius of curvature (r)

a measure of the radius of the circular arc which best approximates the curve at that point

Focal length (for all spherical mirrors)

f=r/2

Key Variable Distances for Geometrical Optics

The focal length (f) is the distance between the focal point (F) and the mirror (for all spherical mirrors,

, where the radius of curvature (r) is the distance between C and the mirror); the distance of the object from the mirror is o; the distance of the image from the mirror is i

Mirror Equation

**(1/o) + (1/i) = 1/f =1/f = 2/r**

can be thought of as infinitely large spherical mirrors.**Plane mirrors***As such, for a plane mirror, r = f = ∞ , and the equation becomes:***(1/o) + (1/i) = 0***or :***i= (-o)**

magnification (m)

** dimensionless value that is the ratio of the image's height to the object's height**

**m= -(i/o)**

*A negative magnification signifies an inverted image, while*-
*a positive value means the image is upright.*

*If |m| < 1, ("absolute value of m is less than 1") the image is reduced; i**f |m| > 1, the image is enlarged; and**if |m| = 1, the image is the same size as the object.*

Ray Diagrams for Concave Spherical Mirror at 3 Different Points

###
- In Figure 10.6a, the object is placed between F and C, and the image produced is real, inverted and magnified.
- In Figure 10.6b, the object is placed at F, and no image is formed because the reflected light rays are parallel to each other. In terms of the mirror equation, we say that the image distance i = ∞ here.
- Figure 10.6c, the object is placed between Fand the mirror, and the image produced is virtual, upright, and magnified.

In general, there are three important rays to draw..

What are they?

###
- For a concave mirror, a ray that strikes the mirror parallel to the horizontal is reflected back through the focal point.
- A ray that passes through the focal point before reaching the mirror is reflected back parallel to the horizontal.
- A ray that strikes the mirror right where the normal intersects it gets reflected back with the same angle (measured from the normal).

Sign Chart for Single MIrrors

**Symbol**

**Positive (+)**

**Negative (-)**

**o**

Object is in front of the mirror (R-side)

Object is behind mirror (V-side)

**i**

Image is in front of mirror (R-side)

Image is behind mirror (V-side)

**r**

Concave mirrors

Convex mirrors

**f**

Concave mirrors

Convex mirrors

**m**

Image is upright (erect)

Image is inverted

Snell's Law of Refraction

**n _{1 }sin θ_{1}= n_{2 }sin θ_{2}**

index of refraction of the medium.

**n=c/v**

- For air, n is essentially equal to 1 because v≈ c.
- But for all other materials on MCAT:
**v < c and n > 1.**

General Bending concepts moving between indecies of different n-values:

###
- when light enters a medium with a higher index of refraction (n2 > n1), it bends towards the normal so that θ 2 < θ 1
- if the light travels into a medium where the index of refraction is smaller (n2 < n1), the light will bend away from the normal so that θ 2 > θ 1.

Total internal reflection

all the light incident on a boundary is reflected back into the original material, results for any angle of incidence greater than the critical angle, θ c

sinθ _{c }=n_{1}/n_{2}

THIN SPHERICAL LENSES

two surfaces that affect the light path

Because light can be coming from either side of a lens, a lens has two focal points (one on each side of the lens) and the focal length can be measured in either direction from its center

basic formulas for finding image distance and magnification

(apply as those from spherical mirrors)

lensmaker's equation

For lenses where the thickness cannot be neglected, the focal length is related to the curvature of the lens surfaces and the index of refraction of the lens by:

**1/f =(n-1) [(1/r _{1)}-(1/r_{2})]**

*where n is the index of refraction of the lens material, r1 is the radius of curvature of the first lens surface and r2 is the radius of curvature of the second lens surface.*

Sign Chart for Single Lenses

**Symbol**

**Positive**

**Negative**

**o**

Object on side of lens light is coming from (V side)

Object on side of lens is going to (R side)

**i**

Image on side of lens light is going to (R side)

Image on side of lens light is coming from (V side)

**f**

Converging lens

Diverging lens

**m**

Image erect

Image inverted

**r**

When on R side (convex surface as seen from side the light is coming from)

When on V side (concave surface as seen from side light is coming from)

power (P).

diopters, where f (the focal length) is in meters and is given by this equation:

**P=1/f**

P has the same sign as f and is, therefore, positive for a converging lens and negative for a diverging lens.

Lenses in contact

series of lenses with negligible distances between them. These systems behave as a single lens with equivalent focal length given by

lenses not in contact,

image of one lens is used to make the object of another lens

dispersion

**n=c/v**

Diffraction

As the slit is narrowed, the light spreads out more. This spreading out of light as it passes through a narrow opening=diffraction

Dark fringes:

**a sin θ = nλ **

*where a is the width of the slit, λ is the wavelength of the incident wave, and θ is the angle made by the line drawn from the center of the lens to the dark fringe and the line perpendicular to the scre*en.

Image of Diffraced Wave

Image of Diffraction Grating and Light Scattering

Interference

Plane-polarized light

ight in which the electric fields of all the waves are oriented in the same direction

Unpolarized light

random orientation of its electric field vectors; sunlight and light emitted from a light bulb are prime examples

Essential Equations for Optics

Photoelectric Effect

work function of the metal

We can calculate the maximum kinetic energy of the ejected electron with the formula:

**K _{max }= hf - W**

The work function is the minimum energy required to eject an electron and is related to the threshold frequency of that metal by

**W=hf _{T}**

_{If the frequency of the incident photon is less than the threshold frequency (f < fT), then no electron will be ejected because the photon doesn't have sufficient energy to dislodge the electron from its atom. But if the frequency of the incident photon is greater than the threshold frequency (f > fT), then an electron will be ejected, and the maximum kinetic energy of the ejected electron will be equal to the difference betweenh f and hfT.}

Energy Levels of Hydrogen

change in energy of an electron due to absorption or emission of a photon.

equation to determine the change in energy of an electron due to absorption or emission of a photon

*delta E = E _{f}-E_{i}*

determine the change in energy of an electron due to absorption or emission of a photon.* *

*hf= absolute value of delta E*

The absolute value sign around Δ E represents the fact that negative frequencies do not exist, so the apparent sign of Δ Eis irrelevant once you know

Bohr Postulates

1. Energy levels of the electron are stable and discrete. They correspond to specific orbits.

2. An electron emits or absorbs radiation only when making a transition from one energy level to another (from one allowed orbit to another).

3. To jump from a lower energy (inner orbit) to a higher energy (outer orbit), an electron must absorb a photon of precisely the right frequency such that the photon's energy (hf) equals the energy difference between the two orbits.

4. When jumping from a higher energy (outer orbit) to a lower energy (inner orbit), an electron emits a photon of a frequency such that the photon's energy (hf) is exactly the energy difference between the two orbits.

Essential Equations of Atomic Phenomena

Exponential Decay

rate:

(where λ is known as the decay constant.)

**Exponential decay**:

**Relation to half life:**