Refraction at a Spherical Surfaces

A convex lens has a focal length of 10 cm. Find the location and nature of the image if a point object is placed on the principal axis at a distance of (a) 9.8 cm, (b) 10.2 cm from the lens.

Assertion: If critical angle of glass-air pair `("μg" = 3/2)` is θ₁ and that of water-air pair `("μw" = 4/3)` is θ₂, then the critical angle for the water-glass pair will lie between θ₁ and θ₂.

Reason: A medium is optically denser if its refractive index is greater.

What type of wavefront will emerge from a (i) point source, and (ii) distance light source?

The equation of refraction at a spherical surface is \[\frac{\mu_2}{\nu} - \frac{\mu_1}{\mu} = \frac{\mu_2 - \mu_1}{R}\]
Taking \[R = \infty\] show that this equation leads to the equation 
\[\frac{\text{ Real  depth }}{\text{ Apparent  depth }} = \frac{\mu_2}{\mu_1}\]
for refraction at a plane surface.

An extended object is placed at a distance of 5.0 cm from a convex lens of focal length 8.0 cm. (a) Draw the ray diagram (to the scale) to locate the image and from this, measure the distance of the image from the lens. (b) Find the position of the image from the lens formula and see how close the drawing is to the correct result.

A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart. If a pin of length 2.0 cm is placed 30 cm from the lens farther away from the mirror, where will the final image form and what will be the size of the final image?

A point source of light is placed at a distance of 2 f from a converging lens of focal length f. The intensity on the other side of the lens is maximum at a distance