An air passenger sitting in an aeroplane flying at a height of 2000 meter from the earth takes photographs of the earth. The focal-length of his camera-lens is 50 cm. The size of the camera-film is (18 × 18)cm2. What maximum area can be covered by the camera?
720 m × 720 m
For camera-lens, we have
Putting these values in lens formula
Solving: v = 0.5 m.
The magnification formula is
The length of the film is 18 cm (= 0.18 m). Hence the maximum possible length of the image is y2 = 0.18 m.
Hence for the maximum length y1 of the object, we have
Hence maximum area of the object = y1 × y1 = 720 m × 720 m.
Glycerine (refractive index 1.4) is poured into a large jar of radius 0.2 m to a depth of 0.1 m. There is a small light source at the centre of the bottom of the jar. Find the area of the surface of glycerine through which the light passes.
A ray of light travelling in glass (refractive index, ang = 3/2) is incident on a horizontal glass-air surface at the critical angle c. If a thin layer of water (refractive index, anw = 4/3) is now poured on the glass-air surface, at what angle will the ray of light emerge into air at the water-air surface?
The radius of curvature of the convex surface of a thin plano-convex lens is 20 cm. Refractive index of the medium of the lens is 1.5. Calculate the focal length of the lens.
The thickness of a plano-convex lens is 4 cm. When it is placed on a horizontal table in such a way that its curved surface be in contact with the table, then the depth of a bottom-point of the lens appears 3 cm. If the lens is inverted so that its plane surface be in contact with the table, then the apparent depth of the centre of the lens-surface is found to be (25/8) cm. Determine the focal-length of the lens.
The focal length of a convex lens in air is 20 cm. What will be its focal length if it is immersed in a liquid of refractive index 1.35? Refractive index of glass is 1.50.
A lens made of glass having refractive index 1.5 has a focal length of 50 cm in air. What will be its focal length if it is immersed in a liquid of refractive index 1.2?
A convex lens of glass (refractive index 1.5) has both surfaces of radius of curvature 20 cm. Find its focal length and nature when it immersed in a liquid of refractive index 1.75.
The focal length of a lens of glass (n = 1.5) in air is 0.4 m and in a liquid is 1.2m. Determine the refractive index of the liquid.
The radius of curvature of both the surfaces of a double convex lens is R. The refractive index of the material of the lens is 1.5. When a point-source of light is placed on the principal axis of the lens at a distance of 20 cm in-front of the one surface of the lens, then rays emerge from the other surface normally. Determine the radius of curvature R of each surface of the lens.
The diameter of sun is 1.4 × 109 meter. Determine the diameter of the image of the sun formed by a convex-lens of focal length 1.0 meter. Distance of the sun from the earth is 1.0 × 1011 meter.