The radius of curvature of a plano-convex lens is 20 cm . Refractive index of glass is 1 . 5 . Find the focal length of the lens.

Radius of curvature of plane surface R 1 = ∞ Radius of curvature of curved convex surface R 2 = − 20 cm Refractive index of material of lens μ = 1 . 5 Using lens maker formula : f 1 = ( μ − 1 ) 1 R 1 − 1 R 2 ∴ 1 f = ( 1 . 5 − 1 ) 1 ∞ − 1 − 20 ⟹ f = 40 cm Hence, required focal length is 40 cm .

A 5 cm long object is placed in front of a concave mirror of radius of curvature 40 cm . The distance of object from mirror is 40 cm . Find the distance and size of the image.

Focal length f = R 2 = - 40 2 = − 20 cm , using sign convention for concave mirror Object distance u = − 5 cm Image distance v = ? Using mirror formula 1 f = 1 v + 1 u − 1 20 = 1 v − 1 5 v = 6 . 67 cm Magnification(M) = h i h o = − v u = - 20 - 3 × 5 = 1 . 33 ⇒ h i = 20 3 = 6 . 67 cm Hence.the position of image is at 6 . 67 cm behind the mirror and size of the image is 6 . 67 cm .

Derive the expression for combined focal length of two thin lenses kept in contact.

Let two thin lenses L 1 and L 2 of focal lengths f 1 and f 2 be put in contact. O is a point object at a distance u from the lens L 1 Its image is formed at I after refraction through the two lenses at a distance v from the combination. The lens L1 forms the image of O at I ' , I ' then serves as a virtual object for the lens L 2 which forms a real image at I. Now, we know that by lens formula 1 v - 1 u = 1 f Applying this relation for refraction at the lens L 1 of focal length f 1 can written as 1 v ' - 1 u = 1 f 1 . . . . . . ( 1 ) For refraction at the lens L 2 u = v ' , v = v For this lens 1 v - 1 v ' = 1 f 2 . . . . ( 2 ) And if is the focal length of the combination, then 1 v - 1 u = 1 F . . . . . . ( 3 ) Adding (1) and (2), we 1 v ' - 1 u + 1 v - 1 v ' = 1 f 1 + 1 f 2 1 F = 1 f 1 + 1 f 2

Write the conditions for obtaining total internal reflection. Write its any two applications.

When a ray of light travels from an optically denser medium to an optically rarer medium and is incident at an angle greater than the critical angle for the two media, the ray totally reflects back into the medium, obeying the laws of reflection. This phenomenon is known as the total internal reflection. For total internal reflection to take place (i) light must travel from a denser medium to a rarer medium and (ii) the angle of incidence inside the denser medium must be greater than the critical angle. i.e., ∠ i > ∠ c .

The magnifying power of objective lens of compound microscope is 06 and eye lens is 05 . Find the net magnifying of compound microscope.

Magnification of objective lens = 06 Magnification of eye lens = 05 Magnification of compound microscope = Magnification of objective lens × Magnification of eye lens = 6 × 5 = 30 Magnification of eye lens = 30