JEE MAIN - Physics (2023 - 31st January Evening Shift - No. 13)
A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$
is poured inside the bucket, then the microscope has to be raised by $30 \mathrm{~cm}$ to focus the object again.
The height of the liquid in the bucket is :
$50 \mathrm{~cm}$
$18 \mathrm{~cm}$
$75 \mathrm{~cm}$
$12 \mathrm{~cm}$
Explanation
Shift $=\left(d-\frac{d}{\mu}\right)=30 \mathrm{~cm}$
$$ \begin{aligned} & \Rightarrow d\left[1-\frac{1}{\frac{5}{3}}\right]=30 \\\\ & \Rightarrow d=\frac{30 \times 5}{2}=75 \mathrm{~cm} \end{aligned} $$
$$ \begin{aligned} & \Rightarrow d\left[1-\frac{1}{\frac{5}{3}}\right]=30 \\\\ & \Rightarrow d=\frac{30 \times 5}{2}=75 \mathrm{~cm} \end{aligned} $$
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