# GRE Subject Test: Physics : Electromagnetics, Waves, and Optics

## Example Questions

### Example Question #1 : Electromagnetics, Waves, And Optics

A particle traveling through glass (index of refraction 1.33) emits Cherenkov radiation. Which of the following is a possible speed of the particle?

Explanation:

Cherenkov radiation is emitted by a particle traveling faster than the phase velocity of light in that medium. Because , the phase velocity of light in the glass is:

This is the minimum velocity of a particle to be emitting Cherenkov radiation in glass. This eliminates all answers except  and The latter is impossible because it is greater than the speed of light in a vacuum, therefore the answer is .

### Example Question #1 : Electromagnetics, Waves, And Optics

A monochromatic beam of  light travels through a material with a phase velocity of . What is the refractive index of the material?

Explanation:

The phase velocity of light through a medium with refractive index  is given by:

Solving this for  and substituting our given value of :

### Example Question #1 : Interference

A double slit experiment is set up with the following parameters: two slits are a separated by a distance . A beam of light with wavelength  shines through the two slits, and is projected onto a screen a distance  from the slits. What is the distance on the screen between the central band and the next band on either side? (This distance is marked '' on the figure).

Explanation:

The condition for constructive interference with double slit diffraction is given by:

Where  is 0, 1, 2, ...

Solving for the angle and using the small angle approximation, we get;

The distance  in the diagram can be related to the other quantities by simple geometry:

Again, with the help of the small angle approximation. Setting the two thetas equal to each other and solving for , we get:

For the central band, , so the  position is also zero. The next band, , yields a distance of:

### Example Question #2 : Electromagnetics, Waves, And Optics

Two waves with frequencies:  are combined. What is the frequency of the resulting beat?

Explanation:

The beat from two combined sound waves is:

### Example Question #1 : Electromagnetics, Waves, And Optics

A beam of light, with wavelength , is normally incident on a transmission diffraction grating. With respect to the incident beam, the first order diffraction maximum occurs at an angle of . What is the number of slits per centimeter on the grating?

Explanation:

The equation describing maxima of a diffraction grating is:

Where d is the separation of slits, which can also be expressed as:

Substituting d into the first equation and making the small angle approximation, one can solve for  (lines per length):

Note that the angle had to be converted from degrees to radians. Finally, the question asks for lines per centimeter, not meter, so the answer becomes .

### Example Question #1 : Electromagnetics, Waves, And Optics

A car's horn has a frequency of . As the car drives away from you, you hear the horn at a frequency of . What is the speed of the car?

Explanation:

The equation for the Doppler effect with frequency for a moving source is given by:

Where  is the speed of sound,  is the speed of the source,  is the stationary frequency and  is the Doppler frequency. Substituting the known values and solving gives us the speed of the car.

### Example Question #1 : Optics

A beam of unpolarized light passes through two linear polarizers whose polarization axes are at an angle theta with each other. The light initially has an intensity , and has an intensity of  after passing through both polarizes. Find ?

Explanation:

Initially unpolarized light passing though a linear polarizer decreases in intensity by a factor of two:

Malus's Law gives the change in intensity of polarized light passing through a linear polarizer in terms of the change in angle of polarization:

Combining the two equations, we get:

Solving for :

### Example Question #1 : Optics

A beam of light travels through a medium with index of refraction  until it reaches an interface with another material, with index of refraction . No light is transmitted into the second material. At what angle (measured from the plane of the interface between the two materials) does the beam hit the second material?

This situation is impossible.

Explanation:

Total internal reflection occurs at the angle:

However, this angle is measured from a line normal to the plane of the interface; the angle we want, therefore, is , which is .

### Example Question #1 : Lenses

The focal length of a thin convex lens is . A candle is placed  to the left of the lens. Approximately where is the image of the candle?

to the left of the lens

to the right of the lens

No image is created

to the right of the lens

to the left of the lens

to the right of the lens

Explanation:

Because the object is beyond 2 focal lengths of the lens, the image must be between 1 and 2 focal lengths on the opposite side. Therefore, the image must be between  on the right side of the lens.

Alternatively, one can apply the thin lens equation:

Where  is the object distance  and  is the focal length . Plug in these values and solve.

### Example Question #2 : Lenses

A candle  tall is placed  to the left of a thin convex lens with focal length . What is the height and orientation of the image created?

, inverted

, upright

, inverted

, upright

No image is created.