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CBSE Class 12 Physics 2015 Delhi Set 1 Paper

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Question : 9 of 26
Marks: +1, -0
Use the mirror equation to show that an object placed between ff and 2f2 f of a concave mirror produces a real image beyond 2f2 f.
OR
Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?
Solution:  
Derivation of the required condition
1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
For concave mirror f<0f < 0 and u<0u < 0
As object lies between ff and 2f2 f
(i) At u=−fu = -f
1v=−1f+1f\frac{1}{v} = -\frac{1}{f} + \frac{1}{f}
⇒v=∞\Rightarrow \quad v = \infty
At u=−2fu = -2 f
⇒1v=−1f+12f=−12f\Rightarrow \quad \frac{1}{v} = -\frac{1}{f} + \frac{1}{2f} = -\frac{1}{2f}
⇒v=−2f\Rightarrow \quad v = -2 f
⇒\Rightarrow Hence, image distance v≥−2fv \geq -2 f
Since, vv is negative therefore the image is real.
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