The vertical angle subtended by two points on a glass block at the objective of a microscope is `20^@`.Calculate the minimum distance between the points if they are just resolved when illuminated by light of wavelength 600 nm. What is the increase in resolving power of the instrument if the objective is immersed in oil of refractive index 1.5?

The semivertical angle of a cone of the rays incident on the objective of the microscope is 20^@ . If lambda = 6600 overset@A , calculate the smallest distance between two points which can be just resolved.

What is the minimum distance between two objects which can be resolved by a microscope having the visual angle of 30^@ when light of wavelength 500 nm is used ?

Convex lens is made of glass of refractive index 1.5 If the radius of curvature of each of the two surfaces is 20 cm find the ratio of the powers of the lens, when placed in air to its power, when immersed in a liquid of refractive index 1.25 .

An isoceles prism of refracting angle 179^@ and refractive index 1.5 is used as a biprism by keeping it 10 cm. away from the slit, The edge of the biprism being parallel to the slit. The slit is illuminated by light of wavelength 500 nm and the screen is 90 cms. away from the biprism. Calculate the location of the centre of 20th dark band and the path difference at this location.

A ray of light is incident on a glass plate of refractive index 1.5. The angle between the reflected and refracted rays is 90^@ . What is the ratio of wavelength of reflected t refracted rays ?

What must be the thickness of a thin film which, when kept near one of the slits shifts the central fringe by 5 mm for incident light of wavelength 5400 A^@ in Young's double slit intereference experiment? The refractive index of the material of the film is 1.1 and the distance between the slits is 0.5 mm.

A man with normal near- point (25c m) reads a book with small print using a magnifying glass L a thin convex lens of focal length 5 cm. (i) What is the closest and the farthest distance at which he can read the book when viewing thorugh the magnifying glass ? (ii) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope ?

A point object ‘O’ is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature 3 mm. The point appeared to be at 5 mm on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is