1
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

Two coherent sources of light interfere. The intensity ratio of two sources is $$1: 4$$. For this interference pattern if the value of $$\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$$ is equal to $$\frac{2 \alpha+1}{\beta+3}$$, then $$\frac{\alpha}{\beta}$$ will be :

A
1.5
B
2
C
0.5
D
1
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $$\lambda$$, calculate the change of microscope's resolving power due to oil and choose the correct option.

A
Resolving power will be $$\frac{1}{4}$$ in the oil than it was in the air.
B
Resolving power will be twice in the oil than it was in the air.
C
Resolving power will be four times in the oil than it was in the air.
D
Resolving power will be $$\frac{1}{2}$$ in the oil than it was in the air.
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

Light travels in two media $$M_{1}$$ and $$M_{2}$$ with speeds $$1.5 \times 10^{8} \mathrm{~ms}^{-1}$$ and $$2.0 \times 10^{8} \mathrm{~ms}^{-1}$$ respectively. The critical angle between them is :

A
$$\tan ^{-1}\left(\frac{3}{\sqrt{7}}\right)$$
B
$$\tan ^{-1}\left(\frac{2}{3}\right)$$
C
$$\cos ^{-1}\left(\frac{3}{4}\right)$$
D
$$\sin ^{-1}\left(\frac{2}{3}\right)$$
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

In Young's double slit experiment, the fringe width is $$12 \mathrm{~mm}$$. If the entire arrangement is placed in water of refractive index $$\frac{4}{3}$$, then the fringe width becomes (in mm):

A
16
B
9
C
48
D
12
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