A spherical lens has two convex surface surfaces of radii 0.8m and1.20m, and the

Question

A spherical lens has two convex surface surfaces of radii 0.8m and1.20m, and the glass from which it is formed has an Index of Refraction of 1.50.
a. Calculate the focal length of the lens. (Note: be certain that you use the proper sign conventions for the two radii of curvature).

b. Find the position of the image of an object located 2.00m from the lens.

c. Determine the magnification and nature of the image if the object is 10cm in height.

Any/all help would be appreciated! Thank you in advance!

Explanation / Answer

Data: Radii: R1 = 0.8 m and R2 = -1.20 m Refractive index, n = 1.50 Object distance, s = 2 m Height of the object, h = 10 cm Solution: (a) From Lens-maker's formula, (1 / f ) = ( n - 1) [ ( 1 / R1 ) - ( 1 / R2 ) ] ( 1 / f ) = (1.50 - 1) [ ( 1 / 0.8 ) + ( 1 / 1.20 ) ] ( 1 / f ) = ( 0.50 ) * 2.083 f = 0.96 m Ans: Focal length, f = 0.96 m (or) 96 cm (b) From lens-formula, (1/f) = ( 1/s) + ( 1/s') (1/s') = ( 1 / 0.96 ) - ( 1 / 2 ) ( 1 / s' ) = 0.54 s' = 1.85 m Ans: Position of the image, s' = 1.85 m (c) Magnification. m = - s' / s                           = - 1.85 / 2                           = - 0.923 Ans: Magnification, m = - 0.923 Nature of the image: Inverted

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