A) \[d(\theta )\]
B) \[d\,(\theta )\,\,(\mu -1)\]
C) \[d\,(\theta )\,\mu /\mu -1\]
D) \[d\,(\theta )\,\frac{(\mu -1)}{\mu }\]
Correct Answer: D
Solution :
Suppose the displacement be x: Then \[\left( \frac{x}{l} \right)=i-r\] Also, \[\left( \frac{d}{l} \right)=\cos r\] As i is small, so r is also small, hence \[\left( \frac{d}{l} \right)\approx 1\] i.e. \[d\approx 1\] Therefore \[\frac{x}{d}=i-r\] \[x=di\,\,\left( 1-\frac{x}{i} \right)\] Also, for small angles \[\frac{\sin i}{\sin r}\approx \frac{i}{r}=\mu \] \[x=di\,\left( 1-\frac{1}{\mu } \right)\] Put \[i=\theta ,\] we get \[x=\frac{d\theta (\mu -1)}{\mu }\]
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