Question

1 7. An object of height 4 cm is kept at a distance of 30 cm from the pole of a diverging mirror. If the focal length of the mirror is 10 cm, the height of the image formed is​

Answer 1

Given :-

Mirror is diverging mirror (convex mirror)

Height of object is (ho= 4 cm)

Distance of the object is (u = 30 cm)

Focal length (f = 10 cm)

To find :-

Height of image

Solution:-

Firstly let's find the distance of image (v)

According to the sign convention,

u = -30 cm , f= 10 cm .

Substituting the values in mirror formula.

⇛1/v + 1/u = 1/f

⇛1/v -1/30 = 1/10

⇛1/v = 1/10 +1/30

⇛1/v = 3+1/30

⇛1/v = 4 /30

v = 30/4 cm = 7.5 cm

Magnification of mirror -v/u = hi/ho

⇛-7.5/-30 = hi/4

⇛7.5/30 = hi/4

⇛75/300 = hi/4

⇛15/20 = hi/4

⇛3/4 = hi/4

hi = +3cm

So, the Height of image is +3 cm.