Question

Locate the image formed by refraction in the situation shown in figure. The point C is the Centre of curvature

1.$100cm$
2.$50cm$
3.$75cm$
4. $25cm$

Answer 1

Hint: In order to find the solution of this question, we need to find the relationship between the object distance$\left( u \right)$, image distance$\left( v \right)$ and radius of curvature$\left( R \right)$. We have a relation between these parameters of the lens.
Formula used: $\dfrac{{{\mu _2}}}{v} - \dfrac{{{\mu _1}}}{u} = \dfrac{{{\mu _2} - {\mu _1}}}{R}$where ${\mu _1}$ and ${\mu _2}$ are refractive indices of the two media as shown in figure. $u = $object distance $v = $image distance,$R = $Radius of curvature.

Complete step-by-step solution:
We use some sign convention to substitute the above formula.
We use the negative sign for the left side of the pole and the positive sign for the right side of the pole.
The value provided in the question according to sign convention we have:
${\mu _2} = 1.5$, ${\mu _1} = 1$, $u = - 25cm$, $R = 20cm$
We need to find the value of image distance,$\left( v \right) = $?
Substituting the above value given in the question within the equation mentioned above:
$ \Rightarrow \dfrac{{{\mu _2}}}{v} - \dfrac{{{\mu _1}}}{u} = \dfrac{{{\mu _2} - {\mu _1}}}{R} \\
   \Rightarrow \dfrac{{1.5}}{v} - \dfrac{1}{{ - 25}} = \dfrac{{1.5 - 1}}{{20}} \\
   \Rightarrow \dfrac{{1.5}}{v} + \dfrac{1}{{25}} = \dfrac{{0.5}}{{20}} \\
   \Rightarrow \dfrac{{1.5}}{v} = \dfrac{1}{{40}} - \dfrac{1}{{25}} \\
   \Rightarrow \dfrac{{1.5}}{v} = \dfrac{{ - 3}}{{200}} \\
   \Rightarrow v = - 100cm $
The image formed by the lens from the pole is at a distance of $100cm$. The negative sign shows that the image formed on the left side of the pole i.e., side of the object.

Note: Some points to be kept in the mind while solving these kinds of questions:
> Always remember the sign convention because it is the key factor to solve any question correctly and it allows you to find the location of the images formed.
> All ray diagrams should be remembered so that the correct representation of the object and image is done accurately.
> Nature of the images formed should be known.