Question

An object 4.0 cm in size, is placed 25.0 cm in front of a concave mirror of focal length 15.0 cm.

1. At what distance from the mirror should a screen be placed in order to obtain a sharp image?
2. Find the size of the image.
3. Draw a ray diagram to show the formation of the image in this case.

Answer 1

Given:

Height of object (h_o) = 4 cm

Object distance (u) = −25 cm

Focal length (Concave mirror) (f) = −15 cm

(i) Applying mirror formula and substituting the values,

`1/v + 1/u = 1/f`

`1/v = 1/(-15) - 1/(-25)`

`1/v = (-5 = 3)/75`

`v = (-75)/2`

= −37.5 cm

The image is in front of the mirror, as indicated by the negative sign. As a result, the screen needs to be positioned 37.5 cm away from the mirror.

(ii) Applying magnification formula and substituting the values,

`m = (-v)/u = (h_i)/(h_o)`

`m = (-((-75)/2))/(-25) = (h_i)/4`

`h_i = (-75)/((2 xx 25) xx 4)`

h_i = −6 m

The image is placed below the principal axis when the sign is negative. As a result, the image is 6 cm in size.

(iii) The ray diagram showing the formation of image in this case is,