A doctor has prescribed a corrective lens of power + 1.5 D. Find
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A doctor has prescribed a corrective lens of power + 1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?


Here,                    P = + 1.5 D
therefore                         straight f space equals space 1 over straight P space equals space fraction numerator 1 over denominator plus 1.5 space straight D end fraction space equals space plus 10 over 15 space straight m space equals space plus space 0.67 space cm space space space Ans. space
As the focal length is positive, the prescribed lens is converging.
Spherical mirrors are of two types:
(i) Concave mirror: A spherical mirror is concave if it is silvered on the outer bulged surface and reflects light from the inner hollow surface [Fig. (b)]

Here,                    P = + 1.5 D               .
Fig. (a) A spherical shell cut by a plane surface, (b) concave mirror, and (c) convex mirror.
(ii) Convex mirror: A spherical mirror is convex if it is silvered on the inner hollow surface and reflects light from the outer bulged surface.


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An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a sharp focussed image can be obtained? Find the size and the nature of the image.

We are given a concave mirror. 

Here, 
Object size, h = + 7.0 cm
Object distance, u = - 27 cm
Focal length, f = - 18 cm 
Image distance, v = ?

Image size, h' = ? 

Now, using the mirror formula, 

                     1u+1v = 1f

                  1v = 1f-1u 

                      = 1-18-1-27 = -3+254 = -154

i.e.,                  v = -54 cm 

The screen should be placed at a distance of 54 cm on the object side of the mirror to obtain a sharp image. 

Magnification, m = h'h = -vu 

 Image size, 
                        h' = -vhu   

                           =-(-54)×(+7)(-27)= -14 cm 

The image is real, inverted and enlarged in size.

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