Question

AN object is placed 18 cm in front of a spherical mirror. if the image is formed at 4 cm to the right of the mirror, calculate its focal length. is the mirror convex or concave? what is the nature of the image? AND what is the radius of curvature of the mirror?

Answer 1

1/f=1/u+1/v

1/f=1/(-18)+1/(+4)

1/f=-2+9/36

f=36/7

R=2f

m=-v/u

f=+ve so mirror is convex

Answer 2

here object distance (u) = 18 cm and image distance(v)= 4 cm

since the image is formed at right side so it is a virtual and erect image. generally, convex mirror forms virtual and erect image. so it is a convex mirror.

so according to the sign convention the object distance(u) will be in negative.

according to the mirror formula,

1/v+1/u=1/f

1/4+1/(-18)=1/f

1/4-1/18=1/f

lcm is 36

9-2/36=1/f

7/36=1/f

f=36/7 , i.e., 5.1cm

and the radius of curvature is 2f=2*5.1=10.2 cm

focal lenght=5.1cm and radius of curvature= 10.2

hope it helps!!!