PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 23, Problem 17P
To determine

The angle of deviation of the ray.

Expert Solution & Answer
Check Mark

Answer to Problem 17P

The angle of deviation of the ray is 16.5° .

Explanation of Solution

The diagram is shown in figure 1.

PHYSICS, Chapter 23, Problem 17P

To find α , use geometry.

The sum of the angles of the triangle must be 180° .

β+2α=180°

Rewrite the above equation for α .

α=180°β2

Given that the value of β is 30.0° . Substitute 30.0° for β in the above equation to find α .

α=180°30.0°2=75.0°

n1 is a normal. The sum of the angles α and θ1 must be 90° .

θ1=90°α

Here, θ1 is the angle of incidence

Substitute 75.0° for α in the above equation to find θ1 .

θ1=90°75.0°=15.0°

The index of refraction of air is 1.000 and that of crown glass is 1.517 .

Write the Snell’s law.

n1sinθ1=n2sinθ2

Here, n1 is the index of refraction of air and n2 is the index of refraction of crown glass

Rewrite the above equation for θ2 .

θ2=sin1(n1n2sinθ1)

Substitute 1.000 for n1 , 1.517 for n2 and 15.0° for θ1 in the above equation to find θ2 .

θ2=sin1(1.0001.517sin15.0°)=9.823°

In the triangle formed by the ray crossing the prism and the two surfaces of the prism, the angles are (90°θ2) , β and (90°θ3) . The sum of these angles must be equal to 180° .

(90°θ2)+β+(90°θ3)=180°θ2+θ3=β (I)

Rewrite t equation (I) for θ3 .

θ3=βθ2

Substitute 30.0° for β and 9.823° for θ2 in the above equation to find θ3 .

θ3=30.0°9.823°=20.18°

To find the angle θ4 , write the Snell’s law.

n2sinθ3=n1sinθ4

Rewrite the above equation for θ4 .

θ4=sin1(n2n1sinθ3)

Substitute 1.517 for n2 , 1.00 for n1 and 20.18° for θ3 in the above equation to find θ4 .

θ4=sin1(1.5171.00sin20.18°)=31.55°

On entering into the prism, the ray is deviated down by the angle θ1θ2 . As it leaves the prism, it changes direction downward through the angle θ4θ3 .

Write the equation for the net deviation.

δ=θ1θ2+θ4θ3=θ1+θ4(θ2+θ3)

Here, δ is the angle of deviation

Put equation (I) in the above equation.

δ=θ1+θ4β (II)

Conclusion:

Substitute 15.0° for θ1, 31.55° for θ4 and 30.0° for β in equation (II) to find δ .

δ=15.0°+31.55°30.0°=16.5°

Therefore, the angle of deviation of the ray is 16.5° .

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Chapter 23 Solutions

PHYSICS

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