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AIEEE 2005

MCQ (Single Correct Answer)
A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $${4 \over 3}$$ and the fish is $$12$$ $$cm$$ below the surface, the radius of this circle in $$cm$$ is
A
$${{36} \over {\sqrt 7 }}$$
B
$${36\sqrt 7 }$$
C
$${4\sqrt 5 }$$
D
$${36\sqrt 5 }$$

Explanation

$$\sin {\theta _c} = {1 \over \mu } = {3 \over 4}$$

or $$\tan {\theta _c} = {3 \over {\sqrt {16 - 9} }} = {3 \over {\sqrt 7 }} = {R \over {12}}$$



$$ \Rightarrow R = {{36} \over {\sqrt 7 }}\,cm$$
2

AIEEE 2004

MCQ (Single Correct Answer)
A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $${45^ \circ }$$, we conclude that the refractive index $$n$$
A
$$n > {1 \over {\sqrt 2 }}$$
B
$$n > \sqrt 2 $$
C
$$n < {1 \over {\sqrt 2 }}$$
D
$$n < \sqrt 2 $$

Explanation

The incident angle is $${45^ \circ }$$

Incident angle $$ > $$ critical angle, $$i > {i_c}$$

$$\therefore$$ $$\sin i > \sin {i_c}$$ or $$\sin \,45\, > \sin \,{i_c},$$ $$\sin {i_c} = {1 \over n}$$

$$\therefore$$ $$\sin \,{45^ \circ } > {1 \over n}$$ or $${1 \over {\sqrt 2 }} > {1 \over n} \Rightarrow n > \sqrt 2 $$
3

AIEEE 2004

MCQ (Single Correct Answer)
The maximum number of possible interference maximum for slit-separation equal to twice the wavelength in Young's double-slit experiment is
A
three
B
five
C
infinite
D
zero

Explanation

For constructive interference $$d\,\sin \theta = n\lambda $$

given $$d = 2\lambda \Rightarrow \sin \theta = {n \over 2}$$

$$n = 0,1, - 1,2, - 2$$ hence five maxima are possible
4

AIEEE 2004

MCQ (Single Correct Answer)
An electromagnetic wave of frequency $$v=3.0$$ $$MHz$$ passes from vacuum into a dielectric medium with permittivity $$ \in = 4.0.$$ Then
A
wave length is halved and frequency remains unchanged
B
wave length is doubled and the frequency becomes half
C
wave length is doubled and the frequency remains unchanged
D
wave length and frequency both remain unchanged. A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $${4 \over 3}$$ and the fish is $$12$$ $$cm$$ below the surface, the radius of this circle in $$cm$$

Explanation

Frequency remains constant during refraction

$${v_{med}} = {1 \over {\sqrt {{\mu _0}{ \in _0} \times 4} }} = {c \over 2}$$

$${{{\lambda _{med}}} \over {{\lambda _{air}}}} = {{{v_{med}}} \over {{v_{air}}}} = {{c/2} \over c} = {1 \over 2}$$

$$\therefore$$ wavelength is halved and frequency remains unchanged

Questions Asked from Ray & Wave Optics

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