Answered: (1) A ray of light is normally incident… | bartleby

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(1) A ray of light is normally incident on the left face of the quarter-
round prism shown. The ray horizontally enters the glass prism 9
cm above its base and then emerges from its circular surface. If
the index of refraction of the prism is 1.50, find the angle that the
emerging ray makes with respect to the horizontal. State your an-
swer as a number of degrees (rounded to 3 significant figures)
above or below the horizontal.
air
air
ray
9 cm
prism
15 cm

Expert Solution

Step 1

Given,

A light ray is incident on the left plate of the quarter round prism.

The emerging ray can be shown as:

Step 2

From the figure,

$\sin θ = \frac{9}{15} \Rightarrow θ = 36.87 °$

Now using Snell's law we have,

$1.5 \times \sin θ = 1 \times \sin r \Rightarrow \sin r = 0.9 \Rightarrow r = 64.16 °$

From the figure,

$θ + r' = r \Rightarrow r' = 64.16 ° - 36.87 ° = 27.29 ° \approx 27.3 °$

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