The radii of curvature of both the surfaces of a convex lens of focal length '$$\mathrm{f}$$' and focal power '$$\mathrm{P}$$' are equal. One of the surfaces is made plane by grinding. The new focal length and focal power of the lens is respectively

A glass slab has refractive index '$$\mu$$' with respect to air and the critical angle for a ray of light in going from glass to glass to air is '$$\theta$$' If a ray of light is incident from air on the glass with angle of incidence '$$\theta$$', then the corresponding angle of refraction is

'Circle of least confusion' refers to which one of the following defects occurring in images formed by mirrors or lenses?

A plano-convex lens of refractive index ($$\mu_1^{\prime}$$ fits exactly into a plano-concave lens of refractive index $$\mu_2$$. Their plane surface are parallel to each other. 'R' is the radius of curvature of the curved surface of the lenses. The focal length of the combination is