### All GRE Subject Test: Physics Resources

## 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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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).

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

This situation is impossible.

**Correct answer:**

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?

**Possible Answers:**

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

**Correct answer:**

to the right of the lens

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?

**Possible Answers:**

, inverted

, upright

, inverted

, upright

No image is created.

**Correct answer:**

, inverted

First, find the image distance * *from the thin lens equation:

Magnification of a lens is given by:

Where * and * are the image height and object height, respectively. The given object height is , which we can use to solve for the image height:

Because the sign is negative, the image is inverted.

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