Embibe Experts Solutions for Chapter: Ray Optics, Exercise 2: Exercise - 2

In an experiment to determine the focal length $\left(f\right)$ of a concave mirror by the $u-v$ method, a student places the object pin $A$ on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping the eye in line with $PA$. When the student shifts the eye towards left, the image appears to the right of the object pin. Then,

The distance between an object and its doubly magnified image by a concave mirror is 

[Assume $f=$ focal length]

In cases of real images formed by a thin convex lens, the linear magnification is

$\left(\mathrm{I}\right)$ directly proportional to the image distance,

$\left(\mathrm{II}\right)$ inversely proportional to the object distance,

$\left(\mathrm{III}\right)$ directly proportional to the distance of image from the nearest principal focus,

$\left(\mathrm{IV}\right)$ inversely proportional to the distance of the object from the nearest principal focus.

From these, the correct statements are,

A particle is moving towards a fixed convex mirror. The image also moves. If $V_{\mathrm{i}}=$speed of image and $V_{\mathrm{O}}=$speed of the object, then

A small air bubble is trapped inside a transparent cube of the size $12 \mathrm{cm}$. When viewed from one of the vertical faces, the bubble appears to be at $5 \mathrm{cm}$ from it. When viewed from the opposite face, it appears at $3 \mathrm{cm}$ from it.

A parallel beam of light is incident normally on the flat surface of a hemisphere of radius $6 \mathrm{cm}$ and refractive index $1.5$, placed in the air as shown in the figure $\left(\mathrm{i}\right)$. Assume paraxial ray approximation.

A ray is an incident on a refracting surface of refractive index $\mu$ at an angle of incidence $i$ and the corresponding angle of refraction is $r$. The deviation of the ray after refraction is given by $\delta =i-r$. Then, one may conclude that

A convex lens and concave lens are kept in contact and the combination is used for the formation of the image of a body by keeping it at different places on the principal axis. The image formed by this combination of lenses can be