2.) Determine the critical angle for total internal reflection of a material with index of refraction 1.52 in air. (Assume air has an index of refraction of 1. 00.)
2.) Determine the critical angle for total internal reflection of a material with index of refraction 1.52 in air. (Assume air has an index of refraction of 1. 00.)
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Please answer part 2 and 5 (highlighted questions). Show all work and circle your final answers. Thank you in advanced.
Transcribed Image Text:1.) Examine Figure 2 in the Background Information section of this lab. There are
two right triangles in red. These two right triangles share the same hypotenuse
of length h. Using this fact, and a little trigonometry, derive Snell's Law. (Hint:
You will need to substitute in 2 = v/f and v = c/n.)
%3D
Snell's Law: n, sin 0, = n, Sin 0,
Alsin02 =12sin01
sin01/sin02-11/1.23DV2/v1
2.) Determine the critical angle for total internal reflection of a material with index
of refraction 1.52 in air. (Assume air has an index of refraction of 1. 00.)
3.) For Part IV of the lab, you will need to determine the radius of curvature of both
a concave and a convex mirror. In either case, the radius of curvature for a
curved mirror can be determined by considering the following diagram:
where d is the depth of the
Surface of
Mirror
curvature at the center of the
mirror, L is the length of the mirror,
and R is the radius of curvature.
R
L/2
Find an expression for the radius of
curvature R in terms of d and L.
R
Provide a trigonometric or algebraic
reason for each of the following
steps in finding an expression for
the radius of curvature R:
![Step
Reason
Pythagoras Theorem (R is the hypotenuse, s is the
base and L/2 is the height if right triangle)
S^ 2 can be replaced by (R-d)^2 because s=R-d
Rearrangement, L^2 /4 moves to the right hand side
from the second step
By expanding (R-d^ 2
By solving the 4th step, and rearranging the terms
value of R is reached
s2 + (L/2)? = R²
(R-d) + (L/4) = R²
(R- d)? = R? - (L/4)
R2-2Rd +d2 = R? - (L /4)
d² +(L/4)
R =
2d
4.) What is the radius of curvature of a plane mirror? Explain your answer using
the diagram in the previous question and flattening the curvature until the
mirror is flat, what happens to R as this is occurring?
The radius of curvature of a plane mirror is infinite because the plane mirror is part of the
sphere is with an infinite radius.
5.) What does the focal length of a curved mirror depend on? Restate the equation
for the focal length of a mirror.
6.) For Part V of the lab, you will need to determine the radius of curvature of both
a concave and a convex lens.
a.) Consider a concave lens with the following parameters:
a
where a is the lens's width across an end, b is
the width across the middle, L is the length of
the lens, d is the depth of curvature, and R is
the radius of curvature. Find an expression
R
L/2
db
for the radius of curvature R in terms of a, b,
and L. Provide a trigonometric or algebraic
reason for each of the following steps in
finding an expression for the radius of
curvature R:
Step
Reason
d² +(L/4)
R =
Result of Prelab 3, which applies here as well.
2d
d = a-
The Rectangular figure
[(a-b)/4] +(L /4)
(a-b)
(a-b)² +L²
Substitution of step two in step one
R =
Simplifying Step 3
R =
4(a-b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca2f9b55-192d-4d11-af1a-09dd4cdb3489%2F1d229b60-b024-48a4-9ffb-ac2d03a6c106%2Fjja7sn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step
Reason
Pythagoras Theorem (R is the hypotenuse, s is the
base and L/2 is the height if right triangle)
S^ 2 can be replaced by (R-d)^2 because s=R-d
Rearrangement, L^2 /4 moves to the right hand side
from the second step
By expanding (R-d^ 2
By solving the 4th step, and rearranging the terms
value of R is reached
s2 + (L/2)? = R²
(R-d) + (L/4) = R²
(R- d)? = R? - (L/4)
R2-2Rd +d2 = R? - (L /4)
d² +(L/4)
R =
2d
4.) What is the radius of curvature of a plane mirror? Explain your answer using
the diagram in the previous question and flattening the curvature until the
mirror is flat, what happens to R as this is occurring?
The radius of curvature of a plane mirror is infinite because the plane mirror is part of the
sphere is with an infinite radius.
5.) What does the focal length of a curved mirror depend on? Restate the equation
for the focal length of a mirror.
6.) For Part V of the lab, you will need to determine the radius of curvature of both
a concave and a convex lens.
a.) Consider a concave lens with the following parameters:
a
where a is the lens's width across an end, b is
the width across the middle, L is the length of
the lens, d is the depth of curvature, and R is
the radius of curvature. Find an expression
R
L/2
db
for the radius of curvature R in terms of a, b,
and L. Provide a trigonometric or algebraic
reason for each of the following steps in
finding an expression for the radius of
curvature R:
Step
Reason
d² +(L/4)
R =
Result of Prelab 3, which applies here as well.
2d
d = a-
The Rectangular figure
[(a-b)/4] +(L /4)
(a-b)
(a-b)² +L²
Substitution of step two in step one
R =
Simplifying Step 3
R =
4(a-b)
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