Questions in Ray Optics and Optical Instruments

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A plano convex lens is made of glass of refractive index $1.5$. The radius of curvature of its convex surface is $R$. Its focal length is
Two lenses have focal lengths ${{f}_{1}}$ and ${{f}_{2}}$ and their dispersive powers are ${{\omega }_{1}}$ and ${{\omega }_{2}}$ respectively. They will together form an achromatic combination if
The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio $5 : 3$. If the focal length of the concave lens is 15 cm, then the nature and focal length of the other lens would be
A thin double convex lens has radii of curvature each of magnitude 40 cm and is made of glass with refractive index 1.65. Its focal length is nearly
The plane surface of a plano-convex lens of focal length $f$ is silvered. It will behave as
An equiconvex lens of glass of focal length $0.1$ metre is cut along a plane perpendicular to principle axis into two equal parts. The ratio of focal length of new lenses formed is
A lens of refractive index $n$ is put in a liquid of refractive index $n'$ of focal length of lens in air is $f$, its focal length in liquid will be
An object of height 1.5 cm is placed on the axis of a convex lens of focal length 25 cm. A real image is formed at a distance of 75 cm from the lens. The size of the image will be
A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was $4 D$, the power of a cut lens will be
A plane convex lens is made of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is

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