If the distance D between an object and screen is greater than 4 times the focal length f of a convex lens, then there are two positions for which the lens forms an enlarged image and a diminished image respectively. This method is called conjugate foci method. If d is the distance between the two positions of the lens, obtain the equation for focal length of the convex lens.

A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. What is the focal length of the eyepiece.

Two light sources with amplitudes 5 units and 3 units respectively interfere with each other. Calculate the ratio of maximum and minimum intensities.

Two light sources of equal amplitudes interfere with each other. Calculate the ratio of maximum and minimum intensities.

A monochromatic light of wavelength 5000  Å passes through a single slit producing diffraction pattern for the central maximum as shown in the figure. Determine the width of the slit.

A monochromatic light of wavelength of 500 nm strikes a grating and produces fourth order maximum at an angle of 30°. Find the number of slits per centimeter.

The optical telescope in the Vainu Bappu Observatory at Kavalur has an objective lens of diameter 2.3 m. What is its angular resolution if the wavelength of light used is 589 nm?

Find the polarizing angles for
(i) glass of refractive index 1.5 and
(ii) water of refractive index 1.33.

Calculate the power of the lens of the spectacles needed to rectify the defect of nearsightedness for a person who could see clearly up to a distance of 1.8 m.

A person has farsightedness with the far distance he could see clearly is 75 cm. Calculate the power of the lens of the spectacles needed to rectify the defect.