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Q. 54

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 992

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Short Answer

Shown from above in FIGURE P34.54 is one corner of a rectangular box filled with water. A laser beam starts from side A of the container and enters the water at position x. You can ignore the thin walls of the container.

a. If , does the laser beam refract back into the air through side B or reflect from side B back into the water? Determine the angle of refraction or reflection.

b. Repeat part a for .

c. Find the minimum value of x for which the laser beam passes through side B and emerges into the air.

a. The laser beam will reflected back into the same water with angle

b. The laser will refracted into the air with the angle

c. The minimum value of x is

See the step by step solution

Step by Step Solution

Part (a) Step 1: Given information

We have given,

A laser beam will enter from from the A into the water.

We have to find the angle for which it will either reflected or refracted from the point B.

Step 2: Simplify

According to the Snell's law we can say,

Where,

is the refractive index of air which is 1.

the refractive index of water.

Let us consider that the laser fall on the glass such that it will make angle with the side of the glass as shown.

Then, using the geometry we can write,

Then, the angle of incidence will be,

Using the sell's law at the interface, we can write

Now again using the geometry we can find,

Then the critical angle will will found out a the interface,

Since the angle is smaller then the laser beam will reflected back into the water with angle from the law of reflection.

Part (b) Step 1: Given information

We have given,

The laser will fall at the interface at from the side.

We have to find the angle of refraction from the interface B.

Step 2: Simplify

Similarly as part a we can use the geometry to find the ,

Then, the angle of incidence will be,

Using the sell's law at the interface, we can write

Now again using the geometry we can find,

Then the critical angle will will found out a the interface,

Since it is smaller than critical angle then it will refract into air.

then,

Part (c) Step 1: Given information

We have give o find the minimum value of x.

Step 2: Simplify

To minimize the value of x let us consider that the ray will reflect through the interface as shown from side B.

Then, we will find the from the geometry is ,

Now using the Snell's law at the interface A is given by,

Then angle will becomes

Then x will found out as

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