Question

A concave mirror has a focal length of 20 cm. At what distance from the mirror should a 4 cm tall object be placed so that it forms an image at a distance of 30 cm from the mirror? Also calculate the size of the image formed. (Answer with an attachment please.)​

Answer 1

Here v= -30 f= -20 so by applying mirror formula,we will get 1/f - 1/v = 1.u so we will get object distance at -60 cm. And by applying, magnification formula,m= -v/u

We will get 30/-60 = -1/2. So image will be

1) Real,

2). Inverted

3) Size = 1/2 X 4 = 2 cm

Answer 2

Given

Focal length of the concave mirror f = +20 cm

Image distance v = 30 cm

Height of the object h₀ = 4 cm

From mirror formula we have,

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

Reducing the above given values in (A) we get,

(1/u) = (1/20) - (1/30)

(1/u) = (3-2)/60

u = 60 cm

As object is kept in front of the mirror by sign convention we denote object distance u = - 60 cm.

Also we know,

Magnification m = (-v)/u = (h₁)/h₀ -------here h₁ = height of the image.

(-30)/(-60) = (h₁)/4

h₁ = (1/2)× 4 = 2 cm.