Question

प्रश्न-14
[4]
किसी 20 सेमी. फोकस दूरी के उत्तल लेंस के सम्पर्क में रखे 25 सेमी. फोकस दूरी के
अवतल लेंस के संयोजन से बने संयुक्त लेंस की फोकस दूरी क्या है? क्या यह संयोजन
अभिसारी लेंस है, अथवा अपसारी?
What is the focus distance of a combined lens made by combining
a concave lens of 25 cm focus distance placed in contact with a
convex lens of 20 cm focus distance? Whether this combination is
convergent lens or divergent?​

Answer 1

SOLUTION

GIVEN

A concave lens of 25 cm focus distance placed in contact with a convex lens of 20 cm focus distance

TO DETERMINE

• The focus distance of the combined lens

• Whether this combination is convergent lens or divergent

EVALUATION

Here it is given that a concave lens of 25 cm focus distance placed in contact with a convex lens of 20 cm focus distance

We know that Focus distance of a convex lens is positive and of concave lens is negative

$\sf{f_1 = Focus \: distance \: of \: concave \: lens = - 25}$

$\sf{f_2= Focus \: distance \: of \: convex \: lens = + 20}$

Let f = The focus distance of the combined lens

We are aware of the formula that

$\displaystyle \sf{ \frac{1}{f} = \frac{1}{f_1 } + \frac{1}{f_2 } }$

$\displaystyle \sf{ \implies \: \frac{1}{f} = \frac{1}{ - 25 } + \frac{1}{20 } }$

$\displaystyle \sf{ \implies \: \frac{1}{f} = - \frac{1}{ 25 } + \frac{1}{20 } }$

$\displaystyle \sf{ \implies \: \frac{1}{f} = \frac{ - 4 + 5}{ 100 } }$

$\displaystyle \sf{ \implies \: \frac{1}{f} = \frac{ 1}{ 100 } }$

$\displaystyle \sf{ \implies \: f = 100}$

The focus distance of the combined lens = 100 cm

Again

Power of the concave lens

$\displaystyle \sf{P_1 = - \frac{1}{0.25} = - 4 }$

Power of the convex lens

$\displaystyle \sf{P_2 = \frac{1}{0.20} = 5 }$

So the power of the combined lens P is given by

$\displaystyle \sf{P = P_1 +P_2 }$

$\displaystyle \sf{ \implies \: P = - 4 + 5 }$

$\displaystyle \sf{ \implies \: P = + 1 }$

Since focus distance and power of the combined lens are both positive

So combined lens is convergent

FINAL ANSWER

• The focus distance of the combined lens = 100 cm

• The combined lens is convergent

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