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Question: A concave lens is placed in contact with a convex lens of focal length 25 cm. The combinations produ...

A concave lens is placed in contact with a convex lens of focal length 25 cm. The combinations produces a real image at a distance of 80cm, if an object is at a distance of 40 cm, the focal length of concave lens is:

A

-400 cm

B

-200 cm

C

+400 cm

D

+200 cm

Answer

-400 cm

Explanation

Solution

: For the combination of focal length,

Here, u = - 40 cm, v = = 80 cm

∴1f=180−1−40=1+280=380\therefore \frac { 1 } { \mathrm { f } } = \frac { 1 } { 80 } - \frac { 1 } { - 40 } = \frac { 1 + 2 } { 80 } = \frac { 3 } { 80 }

Now, 1f=1f1+1f2⇒1f2=1f−1f1\frac { 1 } { \mathrm { f } } = \frac { 1 } { \mathrm { f } _ { 1 } } + \frac { 1 } { \mathrm { f } _ { 2 } } \Rightarrow \frac { 1 } { \mathrm { f } _ { 2 } } = \frac { 1 } { \mathrm { f } } - \frac { 1 } { \mathrm { f } _ { 1 } }