Example 10.2 - Chapter 10 Class 10 - Light - Reflection and Refraction
Last updated at May 29, 2023 by Teachoo
An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and the size of the image.
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Example 10.2
An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave
mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find
the nature and the size of the image.
Since object is always placed above principal axis
Height of object will be positive
Height of the image = h = + 4 cm
Since object is placed infront of the mirror
Object distance will be negative
Object distance = u = β25 cm
Focus of a concave mirror is in front of the mirror.
β΄ Focal length will be negative
Focal length = f = β15 cm
We need to find distance at which
screen should be placed to obtain sharp image
This distance will be the image distance
Finding Image Distance
Let the image distance = v
Using mirror formula
1/π = 1/π£ + 1/π’
1/π β 1/π’ = 1/π£
1/π£ = 1/π β 1/π’
1/π£ = 1/((β15)) β 1/((β25))
1/π£ = (β1)/15 + 1/25
1/π£ = (β5 + 3)/75
1/π£ = (β2)/75
π£ = (β75)/2
π£ = β37.5 cm
β΄ Screen should be placed at a distance of 37.5 cm
Negative sign means that screen should be placed infront of the mirror
Since image is in front of the mirror,
image is real
Finding size of the image
Let the height of image = hβ
We know that,
Magnification of a mirror = (β(πΌππππ πππ π‘ππππ))/(ππππππ‘ πππ π‘ππππ)
= π£/π’
Also,
Magnification of a mirror = (π»πππβπ‘ ππ ππππππ‘)/(π»πππβπ‘ ππ πππππ)
= β^β²/β
From (1) and (2),
(βπ£)/π’ = β^β²/β
(β (β75/2))/((β25)) = β^β²/4
β^β²/4 = ((β75)/2)/25
β^β²/4 = (β75)/(25 Γ 2)
β^β²/4 = (β3)/2
β^β² = (β3 Γ 4)/2
β^β² = β6 cm
Size of the image is 6 cm
and size of object is 4 cm
β΄ Image is enlarged
Negative sign shows that image is formed below the principal axis,
i.e it is inverted
Hence,
Image is inverted and enlarged
CA Maninder Singh is a Chartered Accountant for the past 13 years and a teacher from the past 17 years. He teaches Science, Economics, Accounting and English at Teachoo
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