Example 10.2 - Chapter 10 Class 10 - Light - Reflection and Refraction (Term 1)
Last updated at Sept. 10, 2019 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 = −25 cm
Focus of a concave mirror is in front of the mirror.
∴ Focal length will be negative
Focal length = f = −15 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/𝑓 = 1/𝑣 + 1/𝑢
1/𝑓 − 1/𝑢 = 1/𝑣
1/𝑣 = 1/𝑓 − 1/𝑢
1/𝑣 = 1/((−15)) − 1/((−25))
1/𝑣 = (−1)/15 + 1/25
1/𝑣 = (−5 + 3)/75
1/𝑣 = (−2)/75
𝑣 = (−75)/2
𝑣 = −37.5 cm
∴ 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 = h’
We know that,
Magnification of a mirror = (−(𝐼𝑚𝑎𝑔𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒))/(𝑂𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒)
= 𝑣/𝑢
Also,
Magnification of a mirror = (𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑂𝑏𝑗𝑒𝑐𝑡)/(𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒)
= ℎ^′/ℎ
From (1) and (2),
(−𝑣)/𝑢 = ℎ^′/ℎ
(− (−75/2))/((−25)) = ℎ^′/4
ℎ^′/4 = ((−75)/2)/25
ℎ^′/4 = (−75)/(25 × 2)
ℎ^′/4 = (−3)/2
ℎ^′ = (−3 × 4)/2
ℎ^′ = −6 cm
Size of the image is 6 cm
and size of object is 4 cm
∴ 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
Made by
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 12 years and a teacher from the past 16 years. He teaches Science, Accounts and English at Teachoo
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