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The distance between the object and its inverted image formed by a concave mirror is 25cm. If the magnification produced by the mirror is -2, use mirror formula to determine the object distance, image distance and focal length of the mirror. Draw a ray diagram to illustrate image formation in this case and also mark the distances on it.
Asked by sharmaayush7777777 | 19 Jun, 2019, 02:22: PM
answered-by-expert Expert Answer
if u is object-to-mirror distance and v is image-to-mirror distance, then magnification m = -v/u = -2  .................(1)
 
Hence, we have , v = 2u .......................(2)
 
since magnification is greater than 1, image is real and inverted, object is placed between focal point F and centre of curvature C .
Image is formed beyond centre of curvature as shown in figure.
 
if distance between image and object is 25 cm, then we have, v - u = 25   or  v = u+25 .................(3)
 
using eqn.(2) and eqn.(3),   2u = u+25   or   u  = 25 cm  ..................(4)
 
Hence using eqn.(2) and (4), we get v = 50 cm
 
focal length of mirror is obtained from mirror equation,  (1/v) + (1/u) = 1/f 
 
Hence   (1/50) + (1/25) = 1/f   or we get  f = 50/3 cm 
Answered by Thiyagarajan K | 19 Jun, 2019, 03:26: PM

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