Two thin lenses, when in contact produces a combination of power +10 D. When they are 0.25 m apart, the power reduces to +6 D. The focal length of the lenses are

Question

Two thin lenses, when in contact produces a combination of power +10 D. When they are 0.25 m apart, the power reduces to +6 D. The focal length of the lenses are (A) 0.125 m and 0.5 m (B) 0.125 m and 1 m (C) 1 m and 0.5 m (D) 0.125 m and 0.4 m

Tardigrade Admin · Accepted Answer

When the lenses are in contact, the power of the system is

P = P_{1} + P_{2}

or

P_{1} + P_{2} = 10 ... (i)

When lenses are separated by a distance

d = 0.25 m = \frac{1}{4} m

The power is

P = P_{1} + P_{2} - d P_{1} P_{2}

\Rightarrow P_{1} + P_{2} - \frac{P _{1} P _{2}}{4} = 6 ... (ii)

On solving Eqs. (i) and (ii), we get

10 - \frac{P _{1} P _{2}}{4} = 6

\Rightarrow P_{1} P_{2} = 16

So,

P_{1} = 8 D

and

P_{2} = 2 D

∴ f_{1} = \frac{1}{8} m = 0.125 m

\Rightarrow f_{2} = \frac{1}{2} m = 0.5 m

Q. Two thin lenses, when in contact produces a combination of power $+ 10 D$ . When they are $0.25 m$ apart, the power reduces to $+ 6 D$ . The focal length of the lenses are

$0.125 m$ and $0.5 m$

$0.125 m$ and $1 m$

$1 m$ and $0.5 m$

$0.125 m$ and $0.4 m$

Q. Two thin lenses, when in contact produces a combination of power +10D. When they are 0.25m apart, the power reduces to +6D. The focal length of the lenses are

0.125m and 0.5m

0.125m and 1m

1m and 0.5m

0.125m and 0.4m

Q. Two thin lenses, when in contact produces a combination of power $+ 10 D$ . When they are $0.25 m$ apart, the power reduces to $+ 6 D$ . The focal length of the lenses are

$0.125 m$ and $0.5 m$

$0.125 m$ and $1 m$

$1 m$ and $0.5 m$

$0.125 m$ and $0.4 m$