Where does an object and its image coincide in a concave mirror?

$(a)$ The refractive index of diamond is $2.42$. What is the meaning of this statement?
$(b)$ Redraw the diagram given below in your answer book and complete the path of the ray.
$(c)$ What is the difference between virtual images produced by concave and convex mirrors?
$(d)$ What does the negative sign in the value of magnification produced by a mirror indicate about an image?

The diagram given below shows an object $O$ and its image $I.$ Copy the diagram and draw suitable rays to locate the lens and its focus. Name the type of lens in this case.

The figure below shows a lens treated as a combination of two prisms and a glass block. $(i)$ Name the lens formed by the combination. $(ii)$ Is the lens converging or diverging? $(iii)$ Draw the refraction of two incident rays to illustrate the property of the lens mentioned by you in part $(ii).$

Which type of an image is formed by a plane mirror?

$(a)$ Define power of a lens and write its $SI$ unit.
$(b)$ $A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from it. Where is the needle placed in front of the lens, if the image size is equal to the object size? Also, find the power of the lens.