Question

please tell me the answer of:-


a concave mirror of focal length 12 cm from the double the image of an object find out two position of object when such a thing is possible
​

Answer 1

Answer:

f=−10cm

Case 1: m=2 ( Image is virtual and erect)

m=−

u

v

2=−

u

v

→v=−2u

v

1

+

u

1

=

f

1

−2u

1

+

u

1

=

−10

1

2u

1

=

10

−1

u=−5cm

Case 2: m=−2 (Image is real and inverted)

m=−

u

v

−2=−

u

v

v=2u

v

1

+

u

1

=

f

1

2u

1

+

u

1

=

−10

1

2u

3

=

10

−1

u=−15cm

Answer 2

f=−20cm and m=+2,−2

For a mirror-

v

1

+

u

1

=

f

1

Multiplying both sides by u, we get-

v

u

+1=

f

u

And, magnification=m=

u

−v

So,

m

−1

+1=

f

u

⟹u=

m

f(m−1)

For, m=2, u=

2

−20(2−1)

=−10cm

For m=−2 , u=

−2

−20(−2−1)

=−30cm