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Chapter 23: Problem 10

Sunlight strikes the surface of a lake at an angle of incidence of \(30.0^{\circ} .\) At what angle with respect to the normal would a fish see the Sun?

Short Answer

Expert verified
Answer: The fish sees the Sun at an angle of approximately 22.1° with respect to the normal.

Step by step solution

01

Understand Snell's Law

Snell's Law states that the ratio of the sine of the angle of incidence (\(\theta_{1}\)) to the sine of the angle of refraction (\(\theta_{2}\)) is equal to the ratio of the refractive indices of the two materials: $$ \frac{\sin{\theta_{1}}}{\sin{\theta_{2}}} = \frac{n_{2}}{n_{1}} $$ In this case, \(n_{1}\) is the refractive index of air (approximated to 1.00), \(n_{2}\) is the refractive index of water (approximately 1.33), and \(\theta_{1}\) is the angle of incidence given in the problem.
02

Calculate the angle of refraction

We can rearrange Snell's Law to solve for the angle of refraction \(\theta_{2}\): $$ \theta_{2} = \arcsin \left( \frac{n_{1}\sin{\theta_{1}}}{n_{2}} \right) $$ Now, we can substitute the known values into this formula to calculate the angle of refraction: $$ \theta_{2} = \arcsin \left( \frac{1.00\sin{30.0^{\circ}}}{1.33} \right) $$
03

Evaluate the expression

Using a calculator, we find that: $$ \theta_{2} \approx \arcsin \left( \frac{0.5}{1.33} \right) \approx 22.1^{\circ} $$
04

Find the angle with respect to the normal

The angle of refraction we just calculated is the angle between the sunlight and the normal. Since the fish sees the Sun at this angle of refraction, the angle with respect to the normal is: $$ \theta_{\text{fish}} = \theta_{2} \approx 22.1^{\circ} $$ So, the fish sees the Sun at an angle of approximately \(22.1^{\circ}\) with respect to the normal.

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Most popular questions from this chapter

Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction \(1.4 ?\) If so, what is the critical angle that allows total internal reflection in the first medium?
A converging lens has a focal length of \(8.00 \mathrm{cm} .\) (a) What are the image distances for objects placed at these distances from the thin lens: \(5.00 \mathrm{cm}, 14.0 \mathrm{cm}\) $16.0 \mathrm{cm}, 20.0 \mathrm{cm} ?$ In each case, describe the image as real or virtual, upright or inverted, and enlarged or diminished in size. (b) If the object is $4.00 \mathrm{cm}$ high, what is the height of the image for the object distances of \(5.00 \mathrm{cm}\) and \(20.0 \mathrm{cm} ?\)
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(a) Sunlight reflected from the still surface of a lake is totally polarized when the incident light is at what angle with respect to the horizontal? (b) In what direction is the reflected light polarized? (c) Is any light incident at this angle transmitted into the water? If so, at what angle below the horizontal does the transmitted light travel?
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