Question

A man 1.8 m tall wishes to see full-length image in a plane mirror. The length of the shortest mirror in which he can see his entire image is  

Solution

Correct option is

0.9 m

 

Consider a man AB 1.8 m tall standing in front of a plane mirror hanging on a wall and let E be the position of his eyes (see fig.) He can see his full length image in the mirror if the rays which start from A and B reach his eyes after reflection from the mirror. Let P and Q be the midpoints of AEand EB respectively. From P and Q draw perpendiculars PM and QN on the mirror. The rays AM and BN will be reflected along ME and NErespectively. These rays enter the observer’s eyes. Thus enabling him to see his full image A’B’. Thus MN is the shortest length of the mirror. Now  

                            MN = PQ = PE + EQ

         

SIMILAR QUESTIONS

Q1

A lamp placed at a distance of 50.0 cm from a screen on one side produces the same illumination as a standard 60 cd candle placed 100 cm away on the other side of the screen. What is the luminous intensity of the lamp?

 

Q2

An observer moves towards a stationary plane mirror at a speed of 4 ms–1. With what speed will his image move towards him?  

Q3

Which mirror should be used to obtain a parallel beam of light from a small lamp?

Q4

Choose the only wrong statement from the following.

Q5

A short linear object of length L lies on the axis of a spherical mirror of focal length f at a distance u from the mirror. Its image has an axial lengthL’ equal to

Q6

Two plane mirrors are placed at right angles to each other. A ray strikes one mirror at an angle of incidence θ such that it is also reflected from the second mirror. Then, the ray reflected from the second mirror will be 

Q7

Two plane mirrors are inclined to each other at an angle of 70o. A ray is incident on one mirror at an angle θ. The ray reflected from this mirror falls on the second mirror from where it is reflected parallel to the first mirror. What is the value of θ? 

Q8

One end of a strip of a plane mirror 2.5 cm in length, is fixed. The other end rests on the top of a small vertical rod. A beam of light is reflected from the mirror and forms a spot on a screen 3 m away from the mirror. If the top of the rod is moved upwards 0.1 mm, what will be the movement of the spot? 

Q9

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second is reflected from the second mirror parallel to the first mirror the angle between the two mirrors is   

Q10

An illuminated object is placed between two plane mirrors mutually perpendicular to each other how many images are formed?