What is the physical significance of the index of refraction of light in terms of its velocity? Prove same geometrically.

7. Two sources of light have candle power 16 and 97 respectively. At what point between them will a screen be equally illuminated by each ?

A glass prism, whose angles are 90°, 45°, 45°, is to be used as a totally reflecting prism. What is the least value possible for its index of refraction?

8. In what respects do heat, sound and light waves differ, and what have they in common? What determines the quality of a sound, its pitch, its intensity? Explain the production of beats. What is the Doppler

effect?

9. When heat was supplied at a constant rate to a block of tin it was found that the temperature rose 2° a second. After the melting point was reached the temperature remained constant for 130 seconds when all the tin was melted. If the specific heat of tin is .054, find its latent heat of fusion.

10. A calorimeter contains 316 gms. of water at 40°. Superheated steam at 110° is passed into the water until the mass of water becomes 336 gms. If the weight of the calorimeter parts in contact with the water is 100 gms., and its specific heat o.04, what is the final temperature of the water? Specific heat of steam is 0.48, latent heat vaporization water at 100° is 536 calories per gram.

11. What would be the disadvantage of a thermometer, the bulk of which contained a very large quantity of mercury.

A perfect engine takes steam from a boiler at 150°C, and exhausts into a condenser at 30°C. Compute the efficiency.

State Boyle's Law.

State Charles' Law.

12. If a lantern slide is 2.5x3 inches, and the projecting lens is of focal length, 16 inches, how far from the lens must the screen be placed to give an image 62.5x75 inches? How far will the lens be from the lantern slide?

Upon what does the focal length of a lens depend ? Upon what does the magnification of a telescope depend?

PHYSICS II.

1. (a) An iron ball weighing 1 lb. is whirled in a vertical circle by a string 3 ft. long. If the tension at the top of the path is 2 lbs., how rapidly will the ball be moving at the bottom of the path?

(b) What will be the tension at the point on the circle which is 2 ft. from the lowest point, measured along the arc?

2. If the ball in question 1 be made to move in a horizontal circle and the tension on the string is 5 lbs., what angle will the string make with the vertical? At what velocity will it be moving?

3. (a) The tension on the slack side of a belt is 150 lbs., the coefficient of friction between the belt and the pulley is .35, and the arc of contact is 200°. What is the tension on the tight side of the belt?

(b) If the pulley is 2 ft. in diameter and is running at 720 R.P.M., what horse-power is being transmitted?

4. (a) A flat circular disk rests on a horizontal plane on of its flat faces. If the coefficient of friction between the disk and plane is 2, what horizontal acceleration may be given to the plane without sliding of the disk on the plane?

(b) The same disk is now placed with its flat sides vertical and in the direction of motion of the plane. If the disk is free to rotate, but is held on a fixed axle so that it rotates about this axle, the pressure on the plane being undiminished, what acceleration may be given to the plane?

(c) The axle is now removed and the disk is free to roll on the plane, what acceleration may be given to the plane?

5. A ball weighing 5 lbs. is hung on a coiled spring and made to oscillate vertically. The period is found to be .5 seconds. How much will the spring be stretched if the ball be hung on to the spring when it is unstretched and dropped?

6. A sphere and cylinder start together and roll down an inclined plane reaching the bottom of the plane at the same instant. If the plane is 12 ft. long and inclined 30° to the horizontal, what initial velocity must be given to the cylinder? (The sphere starts from rest).

7. (a) Define modulus of elasticity. Explain fully the two studied and one method for the determination of each. (b) A shaft 2 inches in diameter is carrying a certain load and twists 5°. It is replaced by a shaft of the same material and length, but 134 inches in diameter. How much will the second shaft be twisted?

8. A cube 2 ft. on an edge hangs from an axis in one edge, and oscillates as a pendulum. With what period will it swing?

9. The flat end of a vertical shaft rests on a plane surface with a total thrust of 5000 lbs. If the radius of the shaft is 2 inches and the coefficient of friction is .04, find the moment of the force necessary to turn the shaft.