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Question

A convex lens of focal length 40cm, a concave lens of focal length 40cm and a concave lens of focal length 15cm are placed in contact. The power of the combination in dioptre is


A

+1.5

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B

-1.5

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C

+6.67

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D

-6.67

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Solution

The correct option is D

-6.67


Step 1: Given data.

The focal length of the convex lens is f1=40cm.

The focal length of the first concave lens is f2=-40cm.

The focal length of the second concave lens is f3=-15cm.

Let the total focal length be F.

Let the power be P

Step 2: Find the total focal length of the lens.

So, 1F=1f1+1f2+1f3.

Substitute the given values in the above relation.

1F=140cm+1-40cm+1-15cm1F=140cm-140cm-115cm1F=-115cm

Step 3: Convert the total focal length into metres.

1F=-115cm-115cm=-10015m

Step 4: Find the power.

As we know, P=1F.

Substitute the value of 1F in the above relation.

P=-10015D=-203D=-6.67D

So, the power of the lens is -6.67.

Therefore, the correct option is (D).


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