1. Given data

• Refractive index of block: $\mu_1 = 1.25 = \dfrac{5}{4}$
• Refractive index of surrounding medium: $\mu_2 = 1$
• A ray enters through the vertical flat face and then strikes the top horizontal surface.

We need the maximum incident angle $\theta$ at the side face such that the ray undergoes total internal reflection (TIR) at the top surface.

2. Refraction at the side face

Let the angle of refraction inside the block at the side face be $r$.

Since the ray is entering from medium $(\mu=1)$ into the block $(\mu=1.25)$, Snell's law gives:

3. Condition for total internal reflection at the top surface

At the top surface, the ray goes from denser medium $(1.25)$ to rarer medium $(1)$.

Critical angle $c$ satisfies:

So,

Now, if the ray makes angle $r$ with the horizontal normal of the side face, then at the top horizontal surface its angle of incidence is:

For just TIR (maximum $\theta$),

Hence,

Using

therefore,

4. Find maximum $\theta$

From Snell's law:

Thus,

5. Check options

• A: $\tan^{-1}(4/3)$ — incorrect
• B: $\sin^{-1}(3/4)$ — correct
• C: $\tan^{-1}(3/4)$ — incorrect
• D: $\cos^{-1}(3/4)$ — incorrect

So the correct option is B.