A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?
The incident ray OA is refracted along BD by the lens. Since the image coincides with the object, the refracted ray BD must retrace its path after reflection from the mirror, i.e., it falls normally on the mirror. Let C be the point on the axis where BD produced meets the axis. It is clear that C is the centre of curvature of the mirror. Also C is the image of the object Oformed by the lens alone.
f = +10 cm and u = –12 cm
The distance v of the image is obtained from the lens formula
Which gives v = –60 cm
Since x = 10 cm, R = v – x = 60 – 10 = 50 cm.
Hence the focal length of the mirror
The principle section of a glass prism is an isosceles triangle ABC with AB= AC. The face AC is silvered. A ray incident normally on face AB, after two reflections, emerges from the base BC in a direction perpendicular to it. What is the ∠BAC of the prism?
A mark is made on the surface of a glass sphere of diameter 10 cm and refractive index 1.5. It is viewed through the glass from a portion directly opposite. The distance of the image of the mark from the centre of the sphere will be
An object and a screen are mounted on an optical bench and a converging lens is placed between them so that a sharp image is received on the screen. The linear magnification of the image is 2.5. The lens is now moved 30 cm nearer the screen and a sharp image is again formed on the screen. The focal length of the lens is
A lamp and a screen are set up 100 cm apart and a convex lens is placed between them. The two positions of the lens forming real images on the screen are 40 cm apart. What is the focal length of the lens?
A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?
An object is placed at a distance of 10 cm from a co-axial combination of two lenses A and B. The combination forms a real image three times the size of the object. If lens B is concave with a focal length of 30 cm, what is the nature and focal length of lens A?
A plano-convex lens acts like a concave mirror of 28 cm focal length when its plane surface is silvered and like a concave mirror of 10 cm focal length when its curved surface is silvered. What is the refractive index of the material of the lens?
A pin is placed 10 cm in front of a convex lens of focal length 20 cm and refractive index 1.5. The surface of the lens farther away from the pin is silvered and has a radius of curvature of 22 cm. How far from the lens is the final image formed?
The radius of curvature of the convex face of a plano-convex lens is 12 cm and its refractive index is 1.5. What is the focal length of the lens?
Two glasses have dispersive powers in the ratio of 2 : 3. These glasses are used in the manufacture of an achromatic objective of focal length 20 cm. What are the focal lengths of the two lenses of the objective?