Question 47 The above lens has a focal length of 10 cm. The object of height 2 mm is placed at a distance of 5 cm from the pole. Find the height of the image. (A) 4 cm (B) 6.67 mm (C) 4 mm (D) 3.33 mm The lens in the above figure is a convex lens.
In a convex lens, focal length is positive
Thus
focal length = f = 10 cm
Also,
Height of Object = h1 = 2mm
= 2/10 cm = 0.2 cm
Object Distance = u = −5 cm
We need to find height of image (h2)
To find height, we flint find image distance V
By lens formula,
1/𝑓 = 1/𝑣 − 1/𝑢
𝟏/𝟏𝟎 = 𝟏/𝒗 − 𝟏/((−𝟓))
1/10 = 1/𝑣 + 1/5
(Negative because it is on left side of lens)
1/10 = 1/𝑣 + 1/5
1/10 − 1/5 = 1/𝑣
(1 − 2)/10 = 1/𝑣
(−1)/10 = 1/𝑦
v = −10 cm
Now,
Find magnification
By v & u
m = 𝑣/𝑢
m = (−10)/(−5)
m = 2 …(1)
By h1 & h2
m = (𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒)/(𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡)
m = ℎ_2/ℎ_1
m = 𝒉_𝟐/(𝟎.𝟐) …(2)
Comparing (1) & (2)
= 2 = 𝒉_𝟐/(𝟎.𝟐)
= 2 × 0.2 = ℎ_2
= 0.4 = ℎ_2
ℎ_2 = 0.4 cm
ℎ_2 = 0.4 × 10 mm
𝒉_𝟐 = 4mm
So, the correct answer is (C)

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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