A spherical mirror forms an erect image three times the size of the object, If the distance between the object and the image is 80 cm. The nature and the focal length of the mirror are

Options

A. concave, 15 cm
B. convex, 30 cm
C. concave, 30 cm
D. convex, 15 cm

Answer

C

Explanation

`m=+3,u=-x`
`m=-(v)/(u)implies3=-(v)/(-x)`
`v=3x`
`v+|u|=80implies3x+x=80`
`x=20`
`u=-x=-20cm`,`v=3x=60cm`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(60)+(1)/(-20)=(1-3)/(60)=-(1)/(30)`
`f=-30cm`