1
AIEEE 2010
+4
-1
An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu _2}\,I,$$ where $${\mu _0}$$ and $${\mu _2}$$ are positive constants and $$I$$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

As the beam enters the medium, it will

A
diverge
B
converge
C
diverge near the axis and converge near the periphery
D
travel as a cylindrical beam
2
AIEEE 2010
+4
-1
An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu _2}\,I,$$ where $${\mu _0}$$ and $${\mu _2}$$ are positive constants and $$I$$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

The speed of light in the medium is

A
minimum on the axis of the beam
B
the same everywhere in the beam
C
directly proportional to the intensity $$I$$
D
maximum on the axis of the beam
3
AIEEE 2009
+4
-1
In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $$u$$ and the image distance $$v,$$ from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $${45^ \circ }$$ with the $$x$$-axis meets the experimental curve at $$P.$$ The coordinates of $$P$$ will be :
A
$$\left( {{f \over 2},{f \over 2}} \right)$$
B
$$\left( {f,f} \right)$$
C
$$\left( {4f,4f} \right)$$
D
$$\left( {2f,2f} \right)$$
4
AIEEE 2009
+4
-1
A transparent solid cylindrical rod has a refractive index of $${2 \over {\sqrt 3 }}.$$ It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.

The incident angle $$\theta$$ for which the light ray grazes along the wall of the rod is :

A
$${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{\scriptstyle {\sqrt 3 }} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} \right)$$
B
$${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{\scriptstyle 2} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {\sqrt 3 }}}} \right)$$
C
$${\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$$
D
$${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} \right)$$
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