# GRE Subject Test: Physics : Optics

## Example Questions

### 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.

, inverted

Explanation:

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.

### Example Question #1 : Lenses

Sirius is a binary star system, consisting of two white dwarfs with an angular separation of 3 arcseconds. What is the approximate minimum diameter lens needed to resolve the two stars in Sirius for an observation at ?

Explanation:

The Rayleigh Criterion gives the diffraction limit on resolution of a particular lens at a particular wavelength:

Where theta is the angular resolution in radians,  is the wavelength of light, and  is the diameter the lens in question. Solving for  and converting 3 arcseconds into radians, one can approximate the diameter to be about :

### Example Question #1 : Mirrors

A reflective sphere has a diameter of . The surface of the sphere makes a convex spherical mirror; what is its focal point?