A car is fitted with a convex side-view mirror of focal length $$20$$ $$cm$$. A second car $$2.8m$$ behind the first car is overtaking the first car at a relative speed of $$15$$ $$m/s$$. The speed of the image of the second car as seen in the mirror of the first one is :

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

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

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 :