Question

Two convex lens each of focal length 50 cm and a
concave lens of focal length 20 cm are placed in
closed contact. The power of combination is
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Answer 1

Answer:

-5D

Explanation:

P

convex

1

=

50

100

=+2D

P

concave

1

=

−50

100

=−2D

P

concave

2

=

−20

100

=−5D

P

eq

=−2−5+2

=−5D

Answer 2

Given :

Focal length of convex lenses (F₁) = 50 cm

Focal length of concave lenses (F₂) = 20 cm

To Find :

The power of combination

Solution :

The focal length of the combination can be given as -

     $\frac{1}{F}$  =   $\frac{1}{F_1}$ + $\frac{1}{F_2}$ + $\frac{1}{F_1}$

⇒   $\frac{1}{F}$  =   $\frac{1}{50} + \frac{1}{-20} + \frac{1}{50}$

⇒   $\frac{1}{F}$  =  $\frac{2}{50}$ $-\frac{1}{20}$

⇒   $\frac{1}{F}$  = $\frac{4 - 5}{100}$

⇒   $\frac{1}{F}$  =  $\frac{-1}{100}$

∴    F  =  -100 cm

Therefore, the focal length of the combination is -100 cm

Thus, The power of the combination = $\frac{100}{F}$

                                                               = $\frac{100}{-100}$

                                                               =  -1 D

Hence, the power of the combination is -1 D.

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