In Young's double slit experiment the two slits are illuminated by light of wavelenght 5890 Å and the distance between the fringes obtained on the screen is 0.2^° . If the whole apparatus is immersed in water then the angular fringe width will be, if the refractive index of water is 4 / 3 .

Correct answer: (B) 0.15^°. w_a=λ / d ⇒ w_a α λ frac (w_a )_water w_a=fracλ_water λ=fracλμ_water λ (w_a )_water =(2 × 3)/4=0.15^°

Q115 / 120 · VITEEE 2018 · Physics

In Young's double slit experiment the two slits are illuminated by light of wavelenght $5890 Å$ and the distance between the fringes obtained on the screen is $0.2^{\circ} .$ If the whole apparatus is immersed in water then the angular fringe width will be, if the refractive index of water is $4 / 3$.

A
$0.30^{\circ}$
Correct answer
B
$0.15^{\circ}$
C
$15^{\circ}$
D
$30^{\circ}$

Solution

$$ \begin{array}{l} \mathrm{w}_{\mathrm{a}}=\lambda / \mathrm{d} \Rightarrow \mathrm{w}_{\mathrm{a}} \alpha \lambda \\ \frac{\left(\mathrm{w}_{\mathrm{a}}\right)_{\text {water }}}{\mathrm{w}_{\mathrm{a}}}=\frac{\lambda_{\text {water }}}{\lambda}=\frac{\lambda}{\mu_{\mathrm{water}} \lambda} \\ \left(\mathrm{w}_{\mathrm{a}}\right)_{\text {water }}=\frac{2 \times 3}{4}=0.15^{\circ} \end{array} $$

Hence, the correct answer is option: 'B'.

Solution

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