Question

A light ray is incident on a glass cylinder (n = 1.5) of radius R, at a height R/2 above an optical axis that goes through the center of the cylinder. a. What is the angle of incidence of the light ray on the glass cylinder in degrees (~30)? b. What is the transmitted angle of the ray into the glass in degrees (~19)? c. Through what angle does the ray bend in degrees? No figure was given.

Answer 1

(a) Let $\theta$ be the angle of incidence

so,

sin $\theta$ = (R/2 / R)

sin $\theta$ = 1/2

$\theta$ = arcsin (1/2)

$\theta$ = 30 degree

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(b) Here, we can use snell's law

sin$\theta$ = 1.5*sin$\beta$

where $\beta$ is angle of transmission

so,

$\beta$ = arcsin ( sin 30 / 1.5)

$\beta$ = 19.47 degree

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(c) Through what angle the light ray bends ???? This question is not clear

what do you mean by bend ???

if it means through what angle the light ray us deviated from its original path, then it should be same as part (b)

Answer 2

Here is a figure of the problem that will help with answering part c. 

Since the angle of incidence is 30 degrees, we can use Snell's Law:

sin(θ) = n*sin(θ - α)

0.5 = n*sin(30 - α)

sin(30 - α) = 0.5/n

n = 1.5

∴α = 30 - arcsin(0.5/1.5)

α = 10.529 degrees