Optics, Relativity, Gravity

1. The longest wavelength that can be observed in the fifth-order spectrum using a diffraction grating with 4000 slits per centimeter is: (A) 500 nm (B) 550 nm (C) 600 nm (D) 650 nm

2. Suppose two space ships approach each other at the speed of light, and each sends a beam of light to warn the other of its approach. From the frame of reference of either space ship, the light will reach the ships: (A) before they collide (B) at the instant they collide (C) after they collide (D) none of these

3.The acceleration of an asteroid due to the Earth’s gravity at a height above the Earth’s surface equal to the radius of the Earth is: (A) about 2.5 m/s2 (B) about 4.9 m/s2 (C) 9.8 m/s2 (D) the acceleration depends on how the meteor is moving.

Answers

1. The longest wavelength in the 5th (K) order spectrum is

$\lambda = distance/n/k =0.01/4000/5 =500 nm$

The correct answer is A) 500 nm

2. The composition of speeds u and v takes place as

$S =((u+v)/1+(u*v/C^2))$

hence there is no speed greater than c

The correct answer is B) at the instant they collide

3. The variation of g with height h is

$g(h)/g0 = 1/(1+h^2/R^2) = 1/(1+1)^2 =0.25$

$g(h) =0.25*g0 = 2.45 m/s^2$

the correct answer is A) about $2.5m/s^2$