A concave mirror has focal length 15 cm. Where should an object be placed in front of the mirror so that the image formed is three times the size of the object?
(i) 7.5 cm
(ii) 10 cm
(iii) 17.5 cm
(iv) 20 cm

Options

A. (i),(ii)
B. (ii),(iii)
C. (ii),(iv)
D. (i),(iii)

Answer

C

Explanation

(i) If image is real `m=-3,u=-x`
`m=-(v)/(u)impliesi-3=-(v)/(-x)`
`v=-3x`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(-3x)+(1)/(-x)=(1)/(-15)`
`(4)/(3x)=(1)/(15)impliesx=20cm`
(ii) If image is virtual, `m=+3,u=-x,v=3x`
`(1)/(3x)+(1)/(-x)=(1)/(15)implies(1-3)/(3x)=(1)/(-15)`
`x=10cm`