Question

A concave mirror has radius of curvature of 24 cm. How far is an object from the mirror if an image that is formed is :

1.) virtual and 3times the size of the object.

2.)real and 3 times the size of the object

3.) real and 1/3 the size of the object ?

Answer 1

Here
Given , R = -24cm
Hence f = R/2 = -12Cm

a) Image is virtual and 3 times larger . Hence u is negative and v is +ve simultaneously.
|v| = 3|u|
so let u = -x
v = +3x
Then substituting in the mirror formula
1/v +1/u = 1/f
We have
1/3x -1/x = -1/12
=> x = 8 cm
:• Distance of the object is 8 cm

b) The image is real and three times larger . Hence u and v both are negative and |v| = 3|u|
so let u = -x ,then v = -3x
then substituting the mirror formula we have
1/-3x -1/x = -1/12
=> x = 16 cm
:• Object should be at 16 cm

c) Image is real and 1/3rd the size of the object . Hence Both u and v are negative and
|v| = |u|/3
So let u = -x
then v = -x/3
Substituting in the mirror formula :-
-3/x -1/x = -1/12
=> x = 48 cm
:• The object should be at 48 cm

Answer 2

Answer:

8cm

Explanation:

R=−24 cm;v=−3u; f=−12 cm

1f=1v+1u=−112=−13u+1u=−u+3u3u2=2u3u2

−3u=2×10

u=−243=−8 cm

u=8 cm