Two transparent media of refractive indices n 1 and n 2 are separated by a spherical…
Physics · Class 12 · CBSE — Ray Optics & Optical Instruments
Two transparent media of refractive indices n1 and n2 are separated by a spherical transparent surface. The rays of light incident on the surface get refracted into the medium on the other side. The laws of refraction are valid at each point of the spherical surface. A lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. The focal length of a lens is determined by the radii of curvature (R1 and R2) of its two surfaces and the refractive index (n) of the medium of the lens with respect to the surrounding medium. Depending on R1 and R2, a lens behaves as a diverging or a converging lens. The ability of a lens to diverge or converge a beam of light incident on it defines its power.
An object is placed at the point B as shown in the figure. The object distance (u) and the image distance (v) are related as
- \(\frac{1}{\text{v}}-\frac{1}{\text{u}}=\left(\frac{\text{n}_2-\text{n}_1}{\text{n}_1}\right) \frac{1}{\text{R}}\)
- \(\frac{1}{\text{v}}-\frac{1}{\text{u}}=\left(\frac{\text{n}_1-\text{n}_2}{\text{n}_2}\right) \frac{1}{\text{R}}\)
- \(\frac{\text{n}_2}{\text{v}}-\frac{\text{n}_1}{\text{u}}=\frac{\left(\text{n}_2-\text{n}_1\right)}{\text{R}}\)
- \(\frac{\text{n}_1}{\text{v}}-\frac{\text{n}_2}{\text{u}}=\frac{\left(\text{n}_1-\text{n}_2\right)}{\text{R}}\)
Answer
(C) n _2 v - n _1 u = ( n _2- n _1 ) R
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