Optics - Practice Problems Flashcards
One leg of a Michelson interferometer contains an evacuated cylinder of length L, =0.25m having glass plates on each end. A gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. If 127 bright fringes pass on the screen when light of wavelength λ=500nm is used, what is n, the index of refraction of the gas? State your answer to the nearest 0.000001 ( one part per million).
�
o find the index of refraction of the gas
�
n, we can use the change in the optical path length caused by introducing the gas into the evacuated cylinder in one leg of the Michelson interferometer. The change in optical path length is related to the number of bright fringes observed.
When a gas is introduced into the evacuated cylinder, the number of bright fringes (
�
N) observed is related to the change in optical path length (
Δ
�
ΔL) and the wavelength of the light (
�
λ) by the formula:
Δ
�
=
�
⋅
�
2
ΔL=N⋅
2
λ
The change in optical path length is also related to the index of refraction of the gas (
�
n), the physical length of the cylinder (
�
L), and the index of refraction of the evacuated cylinder (which is 1, since it’s a vacuum) by:
Δ
�
=
(
�
−
1
)
�
ΔL=(n−1)L
Combining these equations gives:
(
�
−
1
)
�
=
�
⋅
�
2
(n−1)L=N⋅
2
λ
Solving for
�
n:
�
⋅
�
2
�
+
1
n=
L
N⋅
2
λ
+1
Substituting the given values:
127
N=127
�
=
500
nm
=
500
×
1
0
−
9
m
λ=500nm=500×10
−9
m
�
=
0.25
m
L=0.25m
�
=
127
⋅
500
×
1
0
−
9
m
2
0.25
m
+
1
n=
0.25m
127⋅
2
500×10
−9
m
+1
�
=
127
⋅
250
×
1
0
−
9
m
0.25
m
+
1
n=
0.25m
127⋅250×10
−9
m
+1
�
=
127
⋅
250
×
1
0
−
9
0.25
+
1
n=
0.25
127⋅250×10
−9
+1
�
=
31.75
×
1
0
−
6
0.25
+
1
n=
0.25
31.75×10
−6
+1
�
=
127
×
1
0
−
6
+
1
n=127×10
−6
+1
�
=
1.000127
n=1.000127
Therefore, the index of refraction of the gas is approximately
1.000127
1.000127, to the nearest millionth.
Grote Reber was a pioneer in radio astronomy. He constructed a radio telescope with a 8m diameter receiving dish. What was the telescope’s angular resolution for 2m radio waves?
State your answer to nearest 0.001rad.
In the context of telescopes, what does Theta θ represent?
Angular Resolution.
It essentially determines the level of detail that can be observed with an optical instrument. A lower (smaller) value of θ indicates a higher angular resolution, meaning the telescope can distinguish two objects that are very close together in the sky.
The pupil of a cat’s eye narrows to a vertical slit of width 0.75mm in daylight. What is the minimum angular resolution of the cat’s eye? Assume that the average wavelength of the light is 680nm.
State your answer in degrees to the nearest 0.0001o
As a result of his observations, Roemer concluded that eclipses of Io by Jupiter were delayed by 23.6min during a 6 months period as the Earth moved from the point its orbit where it is closest to Jupiter to the diametrically opposite point where it is farthest from Jupiter. Using R= 148.5x106 km as the average radius of the Earth’s orbit around the Sun, calculate the speed of light from these data. State your result in km/s to the nearest km/s
The index of refraction for violet light in silica flint glass is nv=1.68, and that for red is nR= 1.56. What is the angular dispersion of visible light passing through a prism of apex angle A= 57o, when the angle of incidence is 49o. ?
State your answer to the nearest 0.001o
A transparent cylinder of radius R = 2.7 m has a mirrored surface on its right half. A light ray traveling in air is incident on the left side of the cylinder. The incident light ray and exiting light ray are parallel and d = 1.1m. Determine the index of refraction of the material. state your answer to nearest 0.001.
Two lenses made of kinds of glass having different refractive indices n1=1.59 and n2=1.50 are cemented together to form what is called an optical doublet. Optical doublets are often used to correct chromatic aberration in optical devices. The first lens of a doublet has one flat side and one concave side if radius of curvature20cm . The second lens has two convex sides of radius of curvature 20cm. Find the focal length of this optical doublet. State our answer in cm to the nearest 0.01cm
An antelope is at a distance of 16 m from a converging lens of focal length 28 cm. The lens forms an image of the animal. If the antelope runs away from the lens at a speed of 10 m/s, what is the magnitude of the speed with which the image moves ? State your answer in mm/s to the nearest 0.01mm/s.
The object in Figure above is midway between the lens and the mirror, which are 29cm apart. The mirror’s radius of curvature is 16cm, and the lens has focal length of -17.5cm. The object (special lamp) is projecting light only toward the mirror. Locate the distance of the final image (formed by this mirror lens system) from the lens. State your answer in cm to the nearest 0.01 cm.
Figure above shows a thin converging lens for which the radii of curvature are R1 =7.5cm and R2 = -11.0cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8cm. Assume that the lens focal points F1 and F2 are 7.5 cm from the center of the lens. Determine its index of refraction. State your answer to the nearest 0.01.
Figure above shows a thin converging lens in front of a concave spherical mirror with the radius of curvature R = 9.0cm. Assume that the lens focal points F1 and F2 are 6.0 cm from the center of the lens. The lens and mirror are 24.0 cm apart, and an object is placed 5.0cm to the left of the lens. How far from the lens is the position of the final image? State your answer in cm to the nearest 0.1 cm.
Your Answer:
How far above the horizon is the Moon when its image reflected in calm water is completely polarized? (nwater = 1.27). State your answer in degrees to the nearest 0.1 degrees.
How high above the horizon is the Moon when its image reflected in calm water is completely polarized? State your answer to the nearest thousandth of degree.
Take nwater= 1.332, nair=1.00014
An object is located 25cm to the left of a diverging lens having a focal length -19cm. Determine the magnification of the image. State your answer to nearest thousandth of a unit.
