Question

A plane mirror which rotates 104 times per minute reflects light on to a stationary mirror 50 m away. This mirror reflects the light normally so that it strikes the rotating mirror again. The image observed in the rotating mirror is shifted through 2.4 minutes from the position it occupies. When the rotating mirror is stationary, what is the speed of light? 

Solution

Correct option is

 

When the plane mirror is rotated through θ, the image formed by the mirror is rotated through 2θ.

Here                  

                       

                      

Here,

                       

                              

                    

But t = time taken by light to go from M1 to M2 and returned back

                      

From Eqs. (i) and (ii)  

                       

SIMILAR QUESTIONS

Q1

The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale 2 metres distant from it. The distance of the objective lens from the eye lens to see with relaxed eye is:

Q2

A good photographic print is obtained by an exposure of two seconds at a distance of 20 cm from the lamp. The time of exposure required to get an equally good result at a distance of 40 cm is: 

Q3

A camera objective has an aperture diameter d. If the aperture is reduced to diameter d/2, the exposure time under identical conditions of light should be made:   

Q4

A film projector magnifies a 100 cm2 film strip on a screen. If the linear magnification is 4, the area of the magnified film on the screen is:

Q5

The resolution limit of the eye is 1 minute. At a distance x km from the eye, two persons stand with a lateral separation of 3 metre. For the two persons to be just resolved by the naked eye, x should be:

Q6

The minimum light intensity that can be perceived by the eye is about 10–10 watt per metre2. The number of photons of wavelength  metre that must enter the pupil of area 10–4 m2 per sec for vision is approximately equal to:    

Q7

An observer looks at a tree of height 15 metres with a telescope of magnifying power 10. To him the tree appears:  

Q8

The distance between the eye lens and cross-wires in Ramsden’s eye-piece which has a field lens of focal length 1.2 cm is:

Q9

If an astronomical telescope has objective and eye-piece of focal lengths 200 cm and 4 cm respectively, then the magnifying power of the telescope for the normal vision is:    

Q10

A source of light lies on the angle bisector of two plane mirrors inclined at an angle θ, so that the light reflected from one mirror does not each other mirror will be