51. Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerin (which has the same refractive index (= 1.5) as that of glass) then the equivalent focal length is $F_2$. The ratio $F_1 : F_2$ will be ?

50. An equiconvex lens has power P. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be ?

49. A double convex lens has focal length 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is 1.5.

48. Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is ?

47. A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $μ_1$ and $μ_2$ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is ?

46. When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index is ___ ?

45. A concave mirror of focal length ’ $f_1$ ’ is placed at a distance of ’ d ’ from a convex lens of focal length ’ $f_2$ ’. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance ’ d ’ must equal :

44. A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options best describe the image formed of an object of height 2 cm placed 30 cm from the lens?

43. A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is ?

42. A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively ?

41. Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The power of the combination is ?

40. A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the Sun is 1.39 × 109 m and its mean distance from the earth is 1.5 × 1011 m. What is the diameter of the Sun’s image on the paper ?

39. A convex lens and a concave lens, each having same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is ?

38. An equiconvex lens is cut into two halves along (i) XOX and (ii) Y OY as shown in the figure. Let f, f′, f′′ be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively. Choose the correct statement from the following.

38. An equiconvex lens is cut into two halves along (i) XOX and (ii) Y OY as shown in the figure. Let f, f′, f′′ be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively. Choose the correct statement from the following.

37. A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will ?

36. A body is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance ’ d ’ ahead of second wall, then the required focal length will be ?

35. The radius of curvature of a thin plano convex lens is 10 cm (of curved surface) and the refractive index is 1.5 . If the plane surface is silvered, then it behaves like a concave mirror of focal length ?

34. A plano-convex lens is made of material of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is ?

33. A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it ?

32. The focal length of converging lens is measured for violet, green and red colours. It is respectively $f_v, f_g, f_r$. We will get ?