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Question

# A convex lens of focal length 25 cm is cut into two equal parts to obtain two plano-convex lenses which are then joined as shown in Fig. 1. Focal length of this combination is

A
25 cm
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B
12.5 cm
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C
50 cm
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D
100 cm
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Solution

## The correct option is A 25 cmIt is given that for a convex lens is 25 cm thenBy uns maker formula 1f=1n⎡⎢ ⎢ ⎢⎣11e+1e⎤⎥ ⎥ ⎥⎦⇒1f=12n[1R]⇒2f=1n[1e]For lens−11f1=1n⎡⎢ ⎢ ⎢⎣11∞+1R⎤⎥ ⎥ ⎥⎦=1n[1R]=2fSimilarly for lens−21f2=1n⎡⎢ ⎢ ⎢⎣11R+1∞⎤⎥ ⎥ ⎥⎦=1n[1R)=2fFor combination of lens−1 and lens −2As, Peff=P1+P2 [P→ Power of lens]⇒1feff=1f1+1f2⇒1feff=2f+2f⇒1feff=1ffeff=f=25 cmOption A is correct

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