A point object is placed at a distance of 10 cm and its real image is formed at a distance of 20 cm from a concave mirror. If the object is moved by 0.1cm towards the mirror, the image will shift by about(a) 0.4cm away from the mirror(b) 0.4cm towards the mirror(c) 0.8cm away from the mirror
(d) 0.8cm towards the mirror
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answer : option (a) 0.4cm away from the mirror.
formula : object distance, u = -10cm
image distance , v = -20cm [ we took, negative sign because image is real, and we know real image formed by concave mirror in same side of object. ]
a/c to question,
object is moved 0.1cm towards the mirror,
e.g., du = 0.1cm
we have to find shifting of image .
use formula, 1/v + 1/u = 1/f
differentiating both sides,
-dv/v² - du/u² = 0 [ f is constant so, differentiation of f = 0]
or, dv = -(v/u)² du
= -(-20cm/-10cm)²(0.1cm)
= -0.4 cm [ here negative sign indicates that image shift away from the mirror]
hence, it is clear that, image will shift 0.4cm away from the mirror.
formula : object distance, u = -10cm
image distance , v = -20cm [ we took, negative sign because image is real, and we know real image formed by concave mirror in same side of object. ]
a/c to question,
object is moved 0.1cm towards the mirror,
e.g., du = 0.1cm
we have to find shifting of image .
use formula, 1/v + 1/u = 1/f
differentiating both sides,
-dv/v² - du/u² = 0 [ f is constant so, differentiation of f = 0]
or, dv = -(v/u)² du
= -(-20cm/-10cm)²(0.1cm)
= -0.4 cm [ here negative sign indicates that image shift away from the mirror]
hence, it is clear that, image will shift 0.4cm away from the mirror.
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