calculate the position of an object placed in front of a concave mirror of focal length 54cm in oder to give an image which is magnified six times
Answers
Answer:
The screen should be placed at the distance of 63 cm from the object.
Explanation:
Equation of mirror is
(1/v) + (1/u) = 1/f,
where v and u are distances of image and object, respectively and f is focal length.
Magnification equation is
M = (hi/ho) = -(v/u),
hi and ho is height of image and object respectively.
As per new Cartesian comvention, distances from the mirror toward the side of object are negative and distance toward the other side are positive. distances above and below the pricipal axis are positive and negetive respectively.
It is given that the image, as obtained on the screen, is 6 times the size of object. Therefore, image is real, hence inverted.
hi = -6ho
(hi/ho) = -6 = -(v/u)
v = 6u
It is given focal length is 54 cm,
f = -54 (In concave mirror, f is negetive)
(1/v) + (1/u) = 1/f
(1/6u) + (1/u) = -(1/54)
(1/u)[(1/6) + 1] = -(1/54)
(1/u)(7/6) = -(1/54)
54×(7/6) = -u
9 × 7 = -u
63 = -u
u = -63
The screen should be placed at the distance of 63 cm from the object.
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Answer:
63 cm and 45 cm
Hope it's helpful
Explanation:
In this case there are two possible which corresponds to real and virtual image respectively
