Chapter 9: Light Reflection and Refraction

Ans: The light rays parallel to the principal axis converge at a point on the principal axis after reflecting from the concave mirror.

The point of convergence on the principal axis of a concave mirror is called the principal focus of a concave mirror. 

Ans: It is given that,

Radius of curvature of a spherical mirror, $R=20cm$ 

It is known that, 

Radius of curvature is twice the focal length.

$R=2f$ 

$\Rightarrow f=R/2$ 

$\Rightarrow f=\frac{20}{2}$

$\Rightarrow f=10cm$ 

Therefore, the focal length of a spherical mirror with the radius of curvature equal to $20cm$ is $f=10cm$.

Ans: If the object is placed between pole and the principal focus of a concave mirror the image formed is virtual, erect and enlarged.

Erect and enlarged images are not possible in case of convex or plane mirrors.

Ans: If the objects are placed in front of a convex mirror, then the image formed is an erect and diminished image.

In vehicles we need erect images and we need to see as many areas as possible behind the vehicles.

So, a convex mirror is preferred as a rear-view mirror in vehicles.

Ans: It is given that,

Radius of curvature of a convex mirror, $R=32cm$ 

It is known that, 

Radius of curvature is twice the focal length.

$R=2f$ 

$\Rightarrow f=R/2$ 

$\Rightarrow f=\frac{32}{2}$

$\Rightarrow f=16cm$ 

Therefore, the focal length of a convex mirror with the radius of curvature equal to $32cm$ is $f=16cm$.

Ans: It is given that,

Distance of object in front of mirror, $u=-10cm$ (negative sign due to the location of the object in front of the mirror)

Distance of image from mirror, $v=?$

It is known that,

Magnification of a spherical mirror,$m=\frac{{{h}_{i}}}{{{h}_{o}}}=-\frac{v}{u}$ 

where,

${{h}_{i}}$ is the height of the image

${{h}_{o}}$ is the height of the object

Let, ${{h}_{o}}=h$ 

It is given that three times the enlarged real image of the object is produced.

So, ${{h}_{i}}=-3h$ ($-$ due to real image formation)

$\Rightarrow m=-\frac{3h}{h}=-\frac{v}{u}$ 

$\Rightarrow 3=\frac{v}{-10}$ 

$\Rightarrow v=-30cm$(negative sign due to the formation of inverted image)

Therefore, the location of image from the mirror is at a distance of $30cm$ and the nature of the image is inverted.

Ans: When a light ray is travelling from the rarer medium to denser medium, it refracts towards the normal.

Here, the light ray bends towards the normal because the light ray is moving from air(rarer) to water(denser) medium. 

Ans:  It is given that,

Refractive index of glass,$\mu =1.50$ 

Speed of the light in vacuum, $c=3\times {{10}^{8}}m{{s}^{-1}}$

Speed of the light in glass,${{v}_{g}}=?$ 

It is known that,

$\mu =\frac{c}{{{v}_{g}}}$ 

$\Rightarrow 1.5=\frac{3\times {{10}^{8}}m{{s}^{-1}}}{{{v}_{g}}}$ 

$\Rightarrow {{v}_{g}}=\frac{3\times {{10}^{8}}}{1.5}$ 

$\Rightarrow {{v}_{g}}=2\times {{10}^{8}}m{{s}^{-1}}$

Therefore, the speed of light in glass is ${{v}_{g}}=2\times {{10}^{8}}m{{s}^{-1}}$ .

Ans: To find the materials of highest and lowest optical densities check for its refractive index. The one with the highest refractive index will have the highest optical density and the one with lowest refractive index will have the lowest optical density.

The highest optical density is for Diamond i.e., $\mu =2.42$

The lowest optical density is for Air i.e.,$\mu =1.0003$

Ans: It is known that,

Absolute refractive index,$\mu =\frac{c}{{{v}_{m}}}$ 

where,

$c$ is the speed of light in vacuum$=3\times {{10}^{8}}m{{s}^{-1}}$ 

${{v}_{m}}$ is the speed of light in medium

$\Rightarrow \mu \propto \frac{1}{{{v}_{m}}}$ ($c$ is constant)

To compare the speed of light we compare the refractive index. Speed of light and refractive index are inversely proportional i.e., if the refractive index is more than the speed of light is less.

The order of refractive index among kerosene, turpentine oil and water is${{\mu }_{\ker osene}}>{{\mu }_{turpentineoil}}>{{\mu }_{water}}$ .

The order of speed of light becomes ${{\mu }_{\ker osene}}<{{\mu }_{turpentineoil}}<{{\mu }_{water}}$ .

Therefore, the speed of light is fastest in water.