Establish the relation between the focal length $\left(\mathrm{f}\right)$ and radius of curvature $\left(\mathrm{R}\right)$

Draw a ray diagram to show the correction of a myopic eye.The near point of the person with the defective eye is $75 \mathrm{cm}.$from the eye. Find the power of lens required to see clearly at $25 \mathrm{cm}$

For refraction at a convex spherical surface of radius of curvature$\mathrm{R}$ from a medium of refractive index ${\mathrm{n}}_1$ to medium of refractive index ${\mathrm{n}}_2({\mathrm{n}}_2>{\mathrm{n}}_1)$, establish the relation:

$\frac{\mathrm{n}}{\mathrm{v}}-\frac{\mathrm{n}}{\mathrm{u}}=\frac{{\mathrm{n}}_2-{\mathrm{n}}_1}{\mathrm{R}}$.

 What will be behaver of a convex lens of the refractive index $1.47$ when it is immersed in a liquid of refractive index $1.47$?

A concave mirror of focal length $18$cm produces $3$ times magnifies erect image of an object. Find the position of object.

In a combination of lenses in contact, the power of first lens is$+2·5D$ and the focal length of second lens is$-25cm$. Calculate the power or focal length of the lens combination.

In a prism ${\mathrm{r}}_1+{\mathrm{r}}_2 =\mathrm{A}$ and $\mathrm{\delta }=\mathrm{i}+\mathrm{e}-\mathrm{A}$, when the prism is at the position of minimum deviation ${\mathrm{D}}_{\mathrm{m}}$. Show that the refractive index of the material of the prism is:

$\mathrm{\mu }=\frac{\sin \left({\displaystyle \frac{\mathrm{A}+{\mathrm{D}}_{\mathrm{m}}}{2}}\right)}{\sin {\displaystyle \frac{\mathrm{A}}{2}}}$

 Also derive the expression for ${\mathrm{D}}_{\mathrm{m}}$ for small angled prism.

Which optical device can produce optical dispersion and which property is responsible for the dispersion of light? Draw a diagram to show that it is possible to obtain white light again after dispersion.