Chapter 9: Light Reflection and Refraction

Ans: It is known that,

Refractive index of a medium,$\mu =\frac{c}{{{v}_{m}}}$ 

where,

$c$ is the speed of light in vacuum

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

$2.42=\frac{c}{{{v}_{d}}}$

“The refractive index of diamond is $2.42$” means that the speed of light in vacuum is $2.42$ times the speed of light in diamond or the speed of light in diamond is $\frac{1}{2.42}$ times the speed of light in vacuum.

Ans: When $f$ is the focal length in metres of a lens with power $P$ then$P=\frac{1}{f(metres)}$ .

Dioptre is the S.I. unit of power of a lens and is denoted by $D$.

The power of a lens of focal length $1$ metre is defined as $1$ dioptre.

Ans: It is given that,

Distance of image from convex lens,$v=50cm$

Distance of object in front of lens,$u=?$

The image formed is real and inverted. So, the magnification of the lens is $-1$.

Image source: Self-created

It is known that, 

Magnification of a convex lens,$m=\frac{v}{u}$ 

$\Rightarrow -1=\frac{v}{u}$ 

$\Rightarrow -1=\frac{50}{u}$ 

$\Rightarrow u=-50cm$ 

Lens formula:$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ 

$f$ is the focal length of the lens.

$\Rightarrow \frac{1}{f}=\frac{1}{50}-\frac{1}{(-50)}$ 

$\Rightarrow \frac{1}{f}=\frac{1}{50}+\frac{1}{50}$ 

$\Rightarrow \frac{1}{f}=\frac{2}{50}$ 

$\Rightarrow f=\frac{50}{2}$ 

$\Rightarrow f=25cm=0.25m$ 

It is known that,

Power of the lens,$P=\frac{1}{f(metres)}$ 

$\Rightarrow P=\frac{1}{(+0.25)}$ 

$\Rightarrow P=+4D$ 

Therefore, the object distance from the lens is $u=-50cm$ and power of the lens is $P=+4D$.

Ans: It is given that,

Focal length of a concave lens is,$f=-2m$ 

Power of the concave lens,$P=\frac{1}{f(metres)}$ 

$\Rightarrow P=\frac{1}{(-2)}$ 

$\Rightarrow P=-0.5D$ 

Therefore, the power of a concave lens is $P=-0.5D$.

Ans: d) Clay can’t be used to make a lens because it is opaque.

Ans: d) The object is placed between the pole of the mirror and its principal focus when the image formed is virtual, erect and larger than the object in the concave mirror. 

Ans: b) An object should be placed at a distance of twice the focal length of a convex lens to get a real image of the size of the object. 

Ans: a) For a concave lens the primary focus is on the same side as the object and is negative. In the case of a concave mirror, the focus is in front of the mirror and negative. Therefore, the mirror and lens are likely to be concave.

Ans: d) Erect images are produced by both plane and convex mirrors for objects at any position.

Ans: a) When the object is placed between focus and optic centre, magnified and erect images are formed in a convex lens. So, while reading small letters a convex lens is preferred.