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Question #43129

Difficulty: 8/10 | 🟢 Free

The Question

An equiconvex thick glass lens is manufactured with a refractive index $\mu = 2.00 \pm 0.04$ . Both spherical surfaces are ground simultaneously such that their radii of curvature are always identical in magnitude, given by $R = 10.0 \pm 0.2 \text{ cm}$ . The central thickness of the lens is precisely $t = 5.0 \text{ cm}$ (assume the error in thickness is negligible). If the lens is placed in a vacuum, what is the maximum percentage error in its equivalent focal length $f$ ?

Options

A.
$\frac{38}{7} \%$
B.
6 %
C.
$\frac{48}{7} \%$
D.
2 %

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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

Lens Maker’s Formula Constraints|Relative Error Propagation in Powers

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to propagate errors through non-linear optical equations when standard approximations fail.

Students commonly default to the Thin Lens Maker's Formula ( $1/f = (\mu-1)(2/R)$ ), which incorrectly yields a $6\%$ error (Option B).

However, the non-negligible thickness of the lens ( $t=5\text{ cm}$ ) requires the use of Gullstrand's equation for a thick lens.

The trap lies in failing to recognize that the lens thickness couples the sensitivity of the focal length to both the refractive index and the radius of curvature.

By forcing a Taylor series expansion (partial derivatives) of the exact thick lens power equation, the problem discriminates between students who blindly apply standard error formulas and those who understand the differential limits of physical systems.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Lens Maker’s Formula Constraints
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free