Question

Two lenses of power #14 and -4 dioptres are placed in contact What will be the focal length of combination
Options
10 cm
12 5 cm
16 6 cm
83 cm
Clear Response​

Answer 1

Answer:

Given:

Two lenses in which:

1. Power of the first lens= $P_{1}$ = 14 Diopters
2. Power of the second lens = $P_{2}$ = -4 Diopters

To find: The focal length of the combination.

Proof:

According to the question, Power of the combination

= $P_{c}$ =  $P_{1}$ + $P_{2}$                                [ subscript c stands for combination]

⇒ $P_{c}$ = 14 + (-4)

⇒ $P_{c}$ = 14-4

⇒ $P_{c}$ = 10 Diopters---------------------{1}

Now,

• Power = $\frac{1}{focal length}$

⇒ $P_{c}$ = $\frac{1}{f_{c} }$

Substituting the values, we get:

= 10 = $\frac{1}{f_{c} }$

⇒ $f_{c}$ = $\frac{1}{10}}$

⇒ $f_{c}$ = 0.1 metres

But, 1 metre = 100 centimetres

∴ 0.1 metre = (0.1 X 100) centimetres

⇒ $f_{c}$ = 0.1 m = 10 cm

Hence, Focal length of the combination

= (a)  $f_{c}$ = 10 cm

Hope you got that.

Thank You.