An object 5 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of image, it's nature and size.
Answers
O=5cm
u=-20cm
R=30cm
to find f
R=2f =f=2\30
= 15 cm
1\v+1\u=1\f
then u can solve easily
Hey Mate ❤
Your Answer -
Given :
Object distance, u = -20 cm
Object height, h = 5 cm
Radius of curvature, R = 30 cm
Focal length, f = R/2 = 15 cm
☑ Mirror Formula :
According to the mirror formula,
1/v + 1/u = 1/f
1/v = 1/f - 1/u
1/v = 1/15 - ( - 1/20 )
1/v = 1/15 + 1/20
1/v = (3+4)/60
1/v = 7/60
v = 8.57 cm
➡ The positive value of v indicates that the image is formed behind the mirror.
☑ Magnification :
m = - v/u = - ( 8.57/-20) = 0.428
➡ The positive value of magnification indicates that the image formed is virtual.
Now again,
m = h'/h { h' is image height }
h' = m × h
h' = 0.428 × 5 = 2.14 cm
➡ The positive value of h' is indicates that the image formed is erect.
☑ Hence, the image formed is erect, virtual, and smaller in size.
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