Verified Solution • 2025–26 Session moderate

QJEEAdv15Ph2885: JEE Advanced 2015 Physics - Class 12 JEEAdv15Ph2885 Solution: If two structures of same cross-sectional area, but different…

If two structures of same cross-sectional area, but different numeral apertures NA1 and NA2 (NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is

Multiple Choice Options

  • A NA1NA2NA1+NA2{{N{A_1}N{A_2}} \over {N{A_1} + N{A_2}}}
  • B NA1+NA2N{A_1} + N{A_2}
  • C NA1N{A_1}
  • D NA2N{A_2}

Step-by-Step Verified Solution

sin⁡im=n1sin⁡(90−θc)\sin i_m=n_1 \sin \left(90-\theta_c\right)

⇒sin⁡im=n1cos⁡θc\Rightarrow \sin i_m=n_1 \cos \theta_c

⇒NAamp;=n11−sin⁡2θcamp;=n11−n22n12=n12−n22\begin{aligned}\Rightarrow N A &amp; =n_1 \sqrt{1-\sin ^2 \theta_c} \\\\&amp; =n_1 \sqrt{1-\frac{n_2^2}{n_1^2}}=\sqrt{n_1^2-n_2^2}\end{aligned}

Substituting the values we get,

NA1=34N A_1=\frac{3}{4}

 and NA2=155=34\text { and } N A_2=\frac{\sqrt{15}}{5}=\sqrt{\frac{3}{4}}

and N A_2 &lt; N A_1

Therefore, the numerical aperture of combined structure is equal to the lesser of the two numerical aperture, which is NA2N A_2 .

Related Learning Resources & Exam Preparation

JEE Advanced PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring