Question

Radius of curvature of convex mirror is 40 cm and the size of the image is twice as that of the
object, then the image distance is
(A) 60 cm
(B) 20 cm
(C) 40 cm
(D) 30 cm​

Answer 1

Answer:

60 will be the answer bcoz image is twice the object

Answer 2

Answer:

60 cm

Explanation:

Given,

Convex mirror

R = 40 cm

size of image ( hi ) = 2 × size of object ( ho )

To find : image distance ( v ) = ?

R = 2f

f = R / 2

= 40 / 2

f = + 20 cm

m = ( hi / ho ) = ( - v / u )

= ( 2 ho / ho ) = ( - v / u )

= ( 2 / 1 ) = ( - v / u )

2 × u = - v × 1

2u = - v

v = - 2u

mirror formula,

( 1 / f ) = ( 1 / v ) - ( 1 / u )

= ( 1 / - 2u ) - ( 1 / u )

= ( - 1 / 2u ) - ( 1 / u )

= ( - 1 / 2u ) - ( 2 / 2u )

= ( - 1 - 2 ) / 2u

( 1 / f ) = - 3 / 2u

( 1 / 20 ) = - 3 / 2u

2u × 1 = - 3 × 20

2u = - 60

u = - 60 / 2

u = - 30

( 1 / f ) = ( 1 / v ) - ( 1 / u )

( 1 / 20 ) = ( 1 / v ) - ( 1 / - 30 )

= ( 1 / v ) - ( - 1 / 30 )

( 1 / 20 ) = ( 1 / v ) + ( 1 / 30 )

( 1 / v ) = ( 1 / 20 ) - ( 1 / 30 )

= ( 3 / 60 ) - ( 2 / 60 )

= ( 3 - 2 ) / 60

( 1 / v ) = 1 / 60

v = + 60 cm

Therefore, the image distance ( v ) is 60 cm.