**Unit 2: Refraction and
Lenses**

**Problem Set B**

The following selection of problems are sample problems. Individual student problem sets will vary since numerical information is randomly-generated.

**Directions:**

For the following problems:

- Compute the unknown quantity and enter the answer in the blank.
- Do not round any computed numbers until the last calculation.
- Unless told otherwise, enter your answers accurate to the second decimal place.
- Unless told otherwise, enter positive numbers for your answers.
- Unless otherwise mentioned, use index of refraction values
from your textbook.

**Problem 1: **

Consider the right triangle shown at the right. If x = 48.1 cm and y = 29.1 cm, then what is the angle theta (in degrees)?

**Problem 2:**

Consider the right triangle shown at the right. If x = 65.6 cm and y = 36.5 cm, then what is the angle theta (in degrees)?

**Problem 3:**

Consider the right triangle shown at the right. If x = 70.6 cm and z = 108.8 cm, then what is the angle theta (in degrees)?

**Problem 4: **

Consider the right triangle shown at the right. If y = 47 cm and z = 64.7 cm, then what is the angle theta (in degrees)?

**Problem 5: **

Consider the right triangle shown at the right. The angle theta is 38 degrees and the side labeled as B is 64.7 cm long. How long (in cm) is the side labeled as A?

**Problem 6: **

(Referring to the problem above.) How long (in cm) is the side labeled as C?

**Problem 7: **

Consider the right triangle shown at the right. The angle theta is 39.7 degrees and the side labeled as L is 41.4 cm long. How long (in cm) is the side labeled as N?

**Problem 8: **

Consider the right triangle shown at the right. The angle theta is 64.8 degrees and the side labeled as N is 55.7 cm long. How long (in cm) is the side labeled as M?

**Problem 9: **

A moving esalator at a department store is 58 meters long. It makes an angle of 20.5 degrees with the horizontal. What is the vertical rise (in meters) of passengers who ride the escalators?

**Problem 10: **

A student stands 93.8 meters from the base of a tall building. Using a protractor, she determines that she must sight along a 34.8 degree angle in order to view the top of the building. How tall (in meters) is the building?

**Problem 11: **

A ray of light in air is incident on the surface of a block of clear ice at an angle of 63.8 degrees with the normal. Part of the light is reflected and part of the light is refracted. Find the angle between the reflected and refracted light rays. Since there are two possible answers (the angle can be measured either clockwise or counter-clockwise from the reflected ray), enter the answer that is less than 180 degrees.

**Problem 12: **

A thick plate of glass (n = 1.69) rests on top of a thick plate of transparent acrylic (n = 1.48). A beam of light in air is incident on the top surface of the glass at an angle theta-i. The beam passes through both the glass and the acrylic and emerges from the acrylic at an angle of 36.4 degrees with respect to the normal. Calculate the value of theta-i (in degrees). A sketch of the light path through the the two plates of refracting material would be helpful. (Assume that both plates are flat and form parallel layers.)

**Problem 13: **

A ray of light from air strikes the midpoint of one face of an equiangular glass prism (n = 1.5) at an angle of incidence of 43.1 degrees. Find the angle of refraction (in degrees) at the point of entry into the glass prism.

**Problem 14: **

(Referring to the previous problem.) The light ray passes through the equiangular prism and emerges from one of the other faces. Determine the angle of refraction (in degrees) of the light ray as it emerges from the glass prism. (HINT: Use geometric principles to determine the angle of incidence and Snell's law to determine the angle of refraction.)

**Problem 15: **

The light beam shown in the diagram below makes an angle of 29.8 degrees with the normal line NN'. in the linseed oil. Determine the angle theta (in degrees) in the diagram. (The index of refraction of linseed oil is 1.5.)

**Problem 16: **

(Referring to the previous problem.) Determine the angle theta-' (in degrees) in the diagram.

**Problem 17: **

A submarine is 325 m horizontally out from the shore and 112 m beneath the surface of the water. A laser beam is sent from the submarine such that it strikes the surface of the water at a point 229 m horizontally out from the shore. If the beam just strikes the top of a building standing directly at the water's edge, find the height (in meters) of the building.

**Problem 18: **

When Crocodile Dundee was young and ignorant of the physics of refraction, villagers would continually laugh at him as he would miss on his attempts at spearing fish. On one such unsuccessful attempt, he was hunting the rare Fishus Targetus. He tried to spear the fish by throwing the spear into the water a horizontal distance of 2.412 meters away from him. The fish was actually under water a horizontal distance of 1.329 meters from the point that the spear entered the water. Dundee aimed for the center of the fish's target (scientists believe that this has contributed to the fact that it is rare). He threw the spear along his line of sight from the height of 1.697 meters. The spear passed over the fish as Dundee aimed directly along his line of sight. Determine the vertical distance by which he missed? That is, find how far the actual fish was below the image of the fish. Enter your answer accurate to the third decimal place.

**Problem 19: **

A narrow beam of ultrasonic waves reflects off the liver tumor as shown in the diagram below. If the wave speed is 10% less in the liver than the surrounding medium, determine the depth (in cm) of the tumor. The angle theta is 58.2 degrees and the distance w is 13.4 cm.

**Problem 20: **

A tall cup is
partially filled with water to a height of 7.8 cm
(H_{water}). The diameter (D) of the cup is 14.64 cm. A
student looks downward just over the left rim of the cup at an angle
of 40.47 degrees with the water's surface (theta). At this angle, the
refraction of light at the water's surface just barely allows her to
see the bottom-right corner of the cup. A sketch (not drawn to scale)
of the path of light is shown at the right. Determine the height of
the cup (H_{cup}) in centimeters.

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