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Chapter 33: Q55P (page 1005)

In Fig. 33-55, a 2.00鈥尘long vertical pole extends from the bottom of a swimming pool to a point 50.0cmabove the water. Sunlight is incident at angle 胃=55.0掳. What is the length of the shadow of the pole on the level bottom of the pool?

Short Answer

Expert verified

The length of the shadow of the pole on the level bottom of the pool is 1.07鈥尘

Step by step solution

01

Given

Angle of incidence 胃=550

l1=0.50鈥尘l2=1.50鈥尘

02

Understanding the concept

We can use Snell鈥檚 law to find the angle of refraction. Then using the geometry of the figure, we can find the length of the shadow of the pole on the level bottom of the pool.

Formula:

n1sin胃1=n2sin胃2

03

Calculate the length of the shadow of the pole on the level bottom of the pool

Ray diagram for the given problem:

According to Snell鈥檚 law,

n1sin胃1=n2sin胃2

But, here

胃1=90鈭�胃=900鈭�550=350

胃2=sin鈭�1n1sin鈥�胃1n2胃2=sin鈭�1(1.0)sin鈥�3501.33胃2=25.550

Now, from the figure,

x=l1tan鈥�胃1x=(0.50鈥�m)tan鈥�350x=0.35鈥尘

And,

L=l2tan鈥�胃2L=(1.50鈥尘)tan鈥�25.550L=0.717~0.72鈥尘

Therefore, the total length of the shadow is

x+L=0.35鈥尘+0.72鈥尘x+L=1.07鈥尘

Therefore, the length of the shadow of the pole on the level bottom of the pool is 1.07鈥尘

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Most popular questions from this chapter

Suppose we rotate the second sheet in Fig. 33-15a, starting with the polarization direction aligned with the y axis(胃=00)and ending with it aligned with the x-axis(胃=90掳). Which of the four curves in Fig. 33-26 best shows the intensity of the light through the three-sheet system during this90掳rotation?

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Question: In the ray diagram of the Figure, where the angles are not drawn to scale, the ray is incident at the critical angle on the interface between materials 2 and 3. Angle 蠒=60.0o, and two of the indexes of refraction are n1=1.70and n2=1.60.(a) Find index of refraction n3and(b) Find angle 胃. (c) If胃 is decreased, does light refract into material 3 ?

Figure:

What is the wavelength of the electromagnetic wave emitted by the oscillator鈥揳ntenna system of the following Fig. 33-3 ifL=0.253渭HandC=25.0pF?

A beam of polarized light is sent into a system of two polarizing sheets. Relative to the polarization direction of that incident light, the polarizing directions of the sheets are at angles 胃for the first sheet and 90掳for the second sheet. If 0.10of the incident intensity is transmitted by the two sheets, what is 胃?
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