CUET · PHYSICS · PYQ PAPER 2023

In double-slits experiment using light of wavelength 550 nm, the angular width of a fringe formed on a distant screen is 0.2°, What is the spacing between the two slits?

A 0.315 mm
B 0.158 cm
C 1.58 cm
D 0.158 mm

Verified Solution

Answer & Solution

Correct Answer

(D) 0.158 mm

Step-by-step Solution

Detailed explanation

\(\theta = 0.2^\circ \times \frac{\pi}{180^\circ} = 0.00349 \text{ rad}\) \(d = \frac{\lambda}{\theta} = \frac{550 \times 10^{-9} \text{ m}}{0.00349 \text{ rad}}\) \(d = 1.5759 \times 10^{-4} \text{ m} = 0.158 \text{ mm}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Match List-I with List-II

List-I (Differential Equations)	List-II (Order and degree)
(A) \(\frac{d y}{d x}+e^y=0\)	(I) order 2, degree not defined
(B) \(\frac{d^2 y}{d x^2}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{3 / 2]}\)	(II) order 2, degree 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+e^{\left(\frac{\text { 临 })}{}\right.}=0\)	(III) order 1, degree 1
(D) \(\frac{d^2 y}{d x^2}+x \frac{d y}{d x}-2 y=\log x ; x>0\)	(IV) order 2, degree 2

Choose the correct answer from the options given below:

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