MHT CET · Physics · Ray Optics

An ink mark is made on a piece of paper on which a glass slab of thickness ' \(t\) ' is placed. The ink mark appears to be raised up through a distance ' \(x\) ' when viewed at nearly normal incidence. If the refractive index of the material of glass slab is ' \(\mu\) ' then the thickness of glass slab is given by

A \(\frac{\mu \mathrm{x}}{\mu-1}\)
B \(\frac{(\mu-1)}{\mu}\)
C \(\frac{\mu-1}{\mu \mathrm{x}}\)
D \(\frac{\mu}{(\mu-1) x}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mu \mathrm{x}}{\mu-1}\)

Step-by-step Solution

Detailed explanation

Here, the normal shift is \(\mathrm{x}\) The formula for the normal shift is
\(
\begin{aligned}
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
\therefore \quad t & =\frac{x \mu}{(\mu-1)}
\end{aligned}
\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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