Question

An object 0.05m is placed at a distance of 0.5m from a concave mirror of radius 0.2m. ​

Answer 1

Answer:

Mirror formula due to Gauss is ( for paraxial rays)

(1/u) + (1/v) = (1/f)

Object distance, u = - 0.5 m.

focal length, f = R/2 = -(0.2/2)=- 0.1 m. (R is radius of curvature ).

Using these values,

-(1/0.5) + (1/v ) = -( 1/0.1) OR

(1/v) = -10 +2 =-8 OR

v=-0.125 m

The magnification for spherical mirror, m =(hi/ho)=- (v/u)=- ( -0.125/-0.5)= -0.25

Now, ho= 0.05m. Therefore,

hi/0.05 =-0.25 OR

hi= - 0.25x0.05=-0.0125m

The image is real, inverted and having size smaller than that of object.

Answer 2

Answer:

Height h of the object =-0.05m

object distance u =-0.5m

Radius of curvature =0.2m

let V be the position of the image,

But, R= 2f, where f is the focal length of the concave mirror

f =R/2

f =0.2/2=-0.1m [-ve for concave mirror ]

using the mirror formula

1/V +1/u=1/f

1/V=1/f-1/u

1/V=(1/-0.1)-(1/-0.5)

1/V=1/0.51/0.1

1/V=2-10

1/V=-8

V=1/-8

V=-0.125m

hence the image is formed at a distance of 0.125m from the mirror

let the height (size) of the image formed b H

H/h=-V/u

H=(V x h/u.) [-ve sign get cancelled ]

H=-0.125x0.05/-0.5

H=0.0125m