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Question #43470

Difficulty: 8/10 | 🟢 Free

The Question

A monochromatic plane wave of wavelength $\lambda$ in vacuum is incident normally on an opaque screen with a circular aperture of diameter $D$ . The screen is coated directly onto the horizontal flat top surface of a transparent encapsulant block of refractive index $n_1 = 2$ . Inside the block, the light strikes a planar solar cell interface having a refractive index $n_2 = \sqrt{2}$ . The normal to the solar cell interface makes an angle $\alpha = 15^\circ$ with the vertical axis of the aperture. To ensure that the entire central maximum (Airy disk) of the diffracted light enters the solar cell without any total internal reflection at the encapsulant-cell interface, what is the minimum required diameter $D$ of the aperture?

Options

A.
$1.22 \lambda$
B.
$2.44 \lambda$
C.
$1.22 \sqrt{2} \lambda$
D.
$0.61 \sqrt{2} \lambda$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Solar Cell Efficiency|Total Internal Reflection (TIR)|Angular Resolution Limit

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of wave optics (diffraction in a dielectric medium) and geometrical optics (Total Internal Reflection on a tilted plane).

The primary trap is the 'etendue/resolution' conflict: students often forget that the diffraction angle depends on the refractive index of the medium ( $\lambda_{med} = \lambda/n_1$ ), leading to an incorrect factor of 2.

A secondary trap is incorrectly mapping the diffraction cone onto the tilted interface, either ignoring the tilt $\alpha$ entirely or miscalculating the maximum angle of incidence as $\theta_{max}$ instead of $\alpha + \theta_{max}$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Semiconductor Electronics: Materials, Devices, and Simple Circuits - Class 12
Concept	Solar Cell Efficiency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free