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Question
An object 4.0 cm in size, is placed 25.0 cm in front of a concave mirror of focal length 15.0 cm.
(i) At what distance from the mirror should a screen be placed in order to obtain a sharp image?
(ii) Find the size of the image.
(iii) Draw a ray diagram to show the formation of the image in this case.
Solution
Given:
Height of object `("h"_"o")` = 4 cm
Object distance `("u")` = -25cm
Focal length `("f")` = -15cm
(i)
Applying mirror formula and substituting the values,
`1/"v" + 1/"u"=1/"f"`
`1/"v" = 1/(-15) - 1/(-25)`
`1/"v" = (-5 + 3)/75`
`"v" = (-75)/2 = -37.5` cm
Negative sign indicates that the image is in front of the mirror.
Therefore, the screen must be placed in front of the mirror at a distance of 37.5 cm.
(ii)
Applying magnification formula and substituting the values,
`"m" = (-"v")/"u" = "h"_"i"/"h"_"o"`
`(-((-75)/2))/-25 = "h"_"i"/4`
`"h"_"i" = (-75)/(2xx25) xx 4`
`"h"_"i" = -6 "cm"`
Negative sign indicates that the image is below the principal axis.
Therefore, the size of the image is 6 cm.
(iii)
The ray diagram showing the formation of image in this case is,
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