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JEE Main 2015 (Offline)

MCQ (Single Correct Answer)
Assuming human pupil to have a radius of $$0.25$$ $$cm$$ and a comfortable viewing distance of $$25$$ $$cm$$, the minimum separation between two objects that human eye can resolve at $$500$$ $$nm$$ wavelength is :
A
$$100\,\mu m$$
B
$$300\,\mu m$$
C
$$1\,\mu m$$
D
$$30\,\mu m$$

Explanation

$$\sin \theta = {{0.25} \over {25}} = {1 \over {100}}$$



Resolving power $$ = {{1.22\lambda } \over {2\mu \sin \theta }} = 30\,\mu m.$$
2

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)
On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :
A
bends down wards
B
bends upwards
C
becomes narrower
D
goes horizontally without any deflection

Explanation

3

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)
A green light is incident from the water to the air - water interface at the critical angle $$\left( \theta \right)$$. Select the correct statement.
A
The entire spectrum of visible light will come out of the water at an angle of $${90^ \circ }$$ to the normal.
B
The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
C
The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
D
The entire spectrum of visible light will come out of the water at various angles to the normal.

Explanation

For critical angle $${\theta _c},$$

$$\sin {\theta _c} = {1 \over \mu }$$

For greater wavelength or lesser frequency $$\mu $$ is less.



So, critical angle would be more, So, they will not suffer reflection and come out at angles less then $${90^ \circ }.$$
4

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)
A thin convex lens made from crown glass $$\left( {\mu = {3 \over 2}} \right)$$ has focal length $$f$$. When it is measured in two different liquids having refractive indices $${4 \over 3}$$ and $${5 \over 3},$$ it has the focal lengths $${f_1}$$ and $${f_2}$$ respectively. The correct relation between the focal lengths is :
A
$${f_1} = {f_2} < f$$
B
$${f_1} > f$$ and $${f_2}$$ becomes negative
C
$${f_2} > f$$ and $${f_1}$$ becomes negative
D
$${f_1}\,$$ and$${f_2}\,$$ both become negative

Explanation

By Lens maker's formula for convex lens

$${1 \over f} = \left( {{\mu \over {{\mu _L}}} - 1} \right)\left( {{2 \over R}} \right)$$

for, $$\mu {L_1} = {4 \over 3},{f_1} = 4R$$

for $$\mu {L_2} = {5 \over 3},{f_2} = - 5R$$

$$ \Rightarrow {f_2} = \left( - \right)ve$$

Questions Asked from Ray & Wave Optics

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