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24/09/2021 8:52 pm
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An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.
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24/09/2021 8:54 pm
The ray diagram is shown below:
Given: h1 = 5 cm, u = -25 cm, f = 10 cm, v = ?
h2 = ?
Applying the formula \frac{1}{f} = \frac{1}{v} - \frac{1}{u}, we get
\frac{1}{v} = \frac{1}{f} + \frac{1}{u}
= \frac{1}{10} + \frac{1}{-25}
= \frac{1}{10} - \frac{1}{25}
= \frac{5 - 2}{50} = \frac{3}{50}
v = \frac{50}{3} = 16.66 cm
Hence, the image is formed at a distance of 16.66 cm from the lens. The positive sign shows that the image is real.
Applying the formula \frac{h_2}{h_1} = \frac{v}{u}, we get
h2 = \frac{v \times h_1}{u} = \frac{50 \times 5}{3 \times -25}
= \frac{-50 \times 5}{3 \times 25} = \frac{-2 \times 5}{3}
= \frac{-10}{3} = -3.33 cm
This is the size of the image. The negative sign shows that the image is inverted.