a thin stick of length f/5 is placed along principle axis of a concave mirror of focal length f such that it's image which is real and elongated just touches the stick .what is the magnification

Asked by amishavasave56.12dgatl | 27th Aug, 2021, 05:25: PM

Expert Answer:

Let u be the distance between pole of concave mirror and front edge of the rod.
It is given that real and elongated image is obtained . Hence the front edge of the rod is
between F and 2F. Since it is given that image touches the rod , mirror-to-image distance
is ( u + ( f/5) ] as shown in figure because length of rod is f/5 .
 
we have mirror equation,  (1/v) + (1/u) = 1/f
 
begin mathsize 14px style fraction numerator 1 over denominator open parentheses u plus begin display style f over 5 end style close parentheses end fraction space plus space 1 over u space equals space 1 over f end style
From above expression , we get a quadratic equation , 5 u2 - 9f u - f2 = 0
 
From above quadratic expression we express u in terms of f as , u = 1.9 f
 
Magnification M = v / u 
 
begin mathsize 14px style M space equals space fraction numerator u space plus space 0.2 space f over denominator u end fraction space equals space fraction numerator 1.9 f space plus 0.2 f over denominator 1.9 end fraction space equals space 1.1 end style

Answered by Thiyagarajan K | 28th Aug, 2021, 08:33: AM