An object 2cm high is placed 10 cm in front of a mirror. what type of mirror and what radius of curvature needed for an upright image that is 4 cm high
Answers
Answer :
U = 10 cm
h = 2 cm
m = height of image ÷ height of the
object
= 4 ÷ 2
= 2
v ÷ u = 2
v = u × 2
= 10 × 2
= 20
v = - 20 CM
Formula
( 1 ÷ f) = ( 1 ÷ v) + ( 1 ÷ u)
f = ( u × v) ÷ ( u + v)
= (-20 × 10 ) ÷ ( -20 + 10)
= ( -200 ) ÷ ( -10 )
= 20 cm
Hence, f = 20
It is a concave mirror.
Given,
Height of the object=2cm
Object is place at 10cm in front of the mirror.
Height of the image=4cm
To Find,
Radius of curvature of the mirror,
type of the mirror.
Solution,
Object distance from the mirror is, u = -10 cm
Height of the object is, h = 2 cm
Then we know,
m = height of image / height of the object
= 4 /2
= 2
So, we got v/u = 2
⇒v = u × 2
⇒v= -10 × 2
⇒v= 20cm
So, v = - 20 CM
We have the formula,
( 1/f) = ( 1/v) + ( 1/u)
f = ( u × v) / ( u + v)
⇒ f= (-20 × 10 ) /( -20 + 10)
⇒f = ( -200 )/( -10 )
⇒f = 20 cm
We have to find out the radius of curvature R,
So formula is R=2f
R=2×20
=40cm
Hence, Radius of curvature of the mirror is 40cm and as its focal length is in positive it is concave in nature.