Sunrays pass through a pinhole in the roof of a hut and produce an elliptical spot on the floor. The minor and major axes of the spot are 6 cm and 12 cm respectively. The angle subtended by the diameter of the sun at our eye is `0.5°`. Calculate the height of the roof.

A telescope consists of two lenses of focal lengths 0.3 m and 3 cm respectively. It is fucussed on moon which subtends an angle of 0.5^@ at the obejctive. Calculate the angle subtended at the eye by the final image in normal adjustment of the telescope.

Two rings are suspended from the points A and B on the ceiling of a room with the help of strings of length 1.2 m each as shown. The points A and B are separated from each other by a distance AB = 1.2 m. A boy standing on the floor throws a small ball so that it passes through the two rings whose diameter is slightly greater than the ball. At the moment when the boy throws the ball, his hand is at a height of 1.0 m above the floor. A stop watch which is switched on at the moment of throwing the ball reads 0.2 s when the ball passes through the first ring and 0.6 s when it passes through the second ring. The angle of projection of the ball is:

Two rings are suspended from the points A and B on the ceiling of a room with the help of strings of length 1.2 m each as shown. The points A and B are separated from each other by a distance AB = 1.2 m. A boy standing on the floor throws a small ball so that it passes through the two rings whose diameter is slightly greater than the ball. At the moment when the boy throws the ball, his hand is at a height of 1.0 m above the floor. A stop watch which is switched on at the moment of throwing the ball reads 0.2 s when the ball passes through the first ring and 0.6 s when it passes through the second ring. The angle of projection of the ball is:

(i) An organ pipe has one end closed and at the other end there is a vibrating diaphragm. The diaphragm is a pressure node. The pipe resonates when the frequency of the diaphragm is 2 KHz. Distance between adjacent nodes is 8.0 cm. When the frequency is slowly reduced, the pipe again resonates at 1.2 KHz. (a) Find the length of the tube. (b) Find the next frequency above 2 KHz at which the pipe resonates. (ii) The figure shows an arrangement for measuring the speed of sound in air. A glass tube is fitted with a movable piston that allows the indicated length L to be adjusted. There is enough gap between the piston and the tube wall to allow the air to pass through it. A speaker is placed near the open end of the tube. A microphone is placed close to the speaker and it is connected to a waveform display. The display is a pure sinusoidal waveform making 750 oscillations in 5 s. Initially, the piston is held at end A and is then slowly pulled back. Loud sound is produced by the tube when L = 50 cm and L = 157 cm . Calculate the speed of sound in air.

On seeing with unaided eye, the visual angle of moon at the eye is 0.6^(@) . The focal lengths of the objective and the eyepiece of a telescope are respectively 200 cm and 5 cm. What will the visual angle on seeing through the telescope?