Question

Two objects A and B, when placed in turn in front of a concave mirror of focal length 7.5 cm give images of equal size. If A is two times the size ofB and is placed at a distance of 15cm from the mirror, find the distance ofB from the mirror

Solution

Correct option is

11.25 cm

 

For a mirror (concave or convex)

We have

                          

And magnification

                            

For object A: u = – 15cm, f = – 7.5 cm   

                             

  

If y1 is the size of the object A and y2 the size of the image, then the magnification is    

                           

For object B: size of object B = y1/2 (given) and size of the image of B = – y1 (inverted)   

                          

or                              c = 2u   

from mirror formula, we have

                           

   

or                               

The object B is a distance of 11.25 cm in front the mirror.

SIMILAR QUESTIONS

Q1

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Q2

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:

Q3

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:    

Q4

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Q5

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:

Q6

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:    

Q7

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? 

Q8

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 

Q9

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that the end closer to the pole is 20 cm away from it. Find the length of the image

                                                        

Q10

A 4.5 cm long needle is placed 12 cm from a convex mirror of focal length 15 cm. find the location and the length of the image of the needle. What happens when the needle is moved farther from the mirror