All GRE Subject Test: Physics Resources
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 ?
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 #2 : 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.
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 #3 : Optics
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?No image is created
to the left of the lens
to the right of the lens
to the left of the lens
to the right of the lens
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 #4 : Optics
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
No image is created.
, inverted
, upright
, upright
, 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.
Example Question #5 : Optics
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
?
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 #6 : Optics
A reflective sphere has a diameter of
. The surface of the sphere makes a convex spherical mirror; what is its focal point?
The focal length of a spherical mirror is one half of the radius, which is one quarter of the diameter. In the case of convex mirrors, the focal point is considered behind the surface, which gives the answer its negative sign.
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