Geometrical Optics — JEE Advanced · 2026 · 17 May 2026 · Paper 2 Question with Solution

Consider two isosceles prisms 1 and 2 with prism angles

A_{1}

and

A_{2}

and refractive indices

n_{1}

and

n_{2}

, respectively, as shown in the figure. The faces

a_{1} b_{1}

and

a_{2} b_{2}

are parallel to each other and perpendicular to the mirror

M

. If a ray of light is incident on the face

a_{1} c_{1}

and emerges from the face

a_{2} c_{2}

, then the correct statement(s) is/are:

(A)If both the prisms are at minimum deviation condition, then $\frac{n _{2}}{n _{1}} = sin (\frac{A _{1}}{2}) / sin (\frac{A _{2}}{2})$ ✓ Correct
(B)If prism 2 is at minimum deviation condition, then $sin i_{1} = n_{2} sin (\frac{A _{2}}{2})$ is always true.
(C)If both the prisms 1 and 2 are thin and are at minimum deviation condition with angles of deviation $δ_{m_{1}}$ and $δ_{m_{2}}$ , respectively, then $θ = \frac{δ _{m 1}}{2 ( n _{1} - 1 )} + \frac{δ _{m 2}}{2 ( n _{2} - 1 )}$ .✓ Correct
(D)If prism 1 is at minimum deviation condition, then $sin i_{2} = n_{1} sin (\frac{A _{1}}{2})$ is always true.✓ Correct

Answer: (A), (C), (D)

Solution

By symmetry, when both prisms are at minimum deviation:

i_{1} = e_{1} = i_{2} = e_{2}

. Applying Snell's law:

sin i_{1} = n_{1} sin (A_{1} /2)

and

sin i_{2} = n_{2} sin (A_{2} /2)

. Since

i_{1} = i_{2}

, we get

\frac{n _{2}}{n _{1}} = \frac{s i n ( A _{1} /2 )}{s i n ( A _{2} /2 )}

. Option (A) is correct.

For option (B), if only prism 2 is at minimum deviation,

i_{2} = e_{2}

but

i_{1} \neq = e_{1}

, so

i_{1} \neq = i_{2}

. Thus

sin i_{1} \neq = n_{2} sin (A_{2} /2)

. Option (B) is incorrect.

For option (C), with both at minimum deviation:

δ_{m 1} = (n_{1} - 1) A_{1}

and

δ_{m 2} = (n_{2} - 1) A_{2}

. The angle

θ = \frac{A _{1}}{2} + \frac{A _{2}}{2} = \frac{1}{2} (\frac{δ _{m 1}}{n _{1} - 1} + \frac{δ _{m 2}}{n _{2} - 1})

. Option (C) is correct.

For option (D), if prism 1 is at minimum deviation,

i_{1} = e_{1} = i_{2}

(by symmetry), so

sin i_{2} = n_{1} sin (A_{1} /2)

. Option (D) is correct.

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · One or more correct options