Question

An object is placed in front of convex surface of a glass piano-convex lens of thickness d = 9.0 cm. The image of that object is formed on the plane surface of the lens serving as a screen. Find: 

(a) the transverse magnification if the curvature radius of the lens's convex surface is R = 2.5 cm; 

(b) the image illuminance if the luminance of the object is L = 7700 cd/m² and the entrance aperture diameter of the lens is D = 5.0 mm; losses of light are negligible.

Answer 1

(a) The formation of the image of a source S, placed at a distance u from the pole of the convex surface of plane-convex lens of thickness d is shown in the figure.

On applying the formula for refraction through spherical surface, we get

But in this case optical path of the light, corresponding to the distance v in the medium is v/n, so the magnification produced will be,

Substituting the values, we get magnification β = - 0-20. 

(b) If the transverse area of the object is A (assumed small), the area of the image is β² A. 

We shall assume that   Then light falling on the Jens is:  from the definition of luminance (See Eqn. (5.1c) of the book; here