A) 30 cm towards the mirror
B) 36 cm away from the mirror
C) 30 cm away from the mirror
D) 36 cm towards the mirror
Correct Answer: B
Solution :
| [b] |
 |
| \[\frac{1}{f}=\frac{1}{{{v}_{1}}}+\frac{1}{u}\] |
| \[-\frac{1}{15}=\frac{1}{{{v}_{1}}}-\frac{1}{40}\] |
| \[\Rightarrow \frac{1}{{{v}_{1}}}=\frac{1}{-15}+\frac{1}{40}\] |
| \[{{v}_{1}}=-24cm\] |
| When object is displaced by 20 cm towards mirror. |
| Now, |
| \[{{u}_{2}}=-20\] |
| \[\frac{1}{f}=\frac{1}{{{v}_{2}}}+\frac{1}{{{u}_{2}}}\] |
| \[\frac{1}{-15}=\frac{1}{{{v}_{2}}}-\frac{1}{20}\] |
| \[\frac{1}{{{v}_{2}}}=\frac{1}{20}-\frac{1}{15}\] |
| \[{{v}_{2}}=-60cm\] |
| So, image shifts away from mirror by \[=60-24=36cm\]. |
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