An object of height 10 cm is placed at the focus of a concave lens. What is the height of the image ?

Options

A. 5 cm
B. 2.5 cm
C. 7.5 cm
D. 12.5 cm

Answer

A

Explanation

For a concave lens, u, v and f are negative.
u = f (given)
`because (1)/(v)-(1)/(u)=(1)/(f)`
`therefore (1)/(v)=(1)/(f)+(1)/(u)= -(1)/(u)-(1)/(u)= -(2)/(u)`
`therefore v=-(u)/(2)`
`therefore " Magnification " M=(I)/(O)=(v)/(u)=(u)/(2u)=(1)/(2)`
`therefore M=(I)/(10)=(1)/(2) therefore 2I=10 therefore I=5 cm`
`therefore ` Height of the image is 5 cm.