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Question
You have two lenses A and B of focal lengths +10 cm and –10 cm, respectively. State the nature and power of each lens. Which of the two lenses will form a virtual and magnified image of an object placed 8 cm from the lens? Draw a ray diagram to justify your answer
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Solution
Given: Focal length of lens A, fA = +10 cm = +0.1 m
Focal length of lens B, FB = −10 cm = −0.1 m
To calculate the power of lens A:-
The power of lens A, P = 1/FA(in metres)
P = 1/ +0.1
∴ P = +10 dioptre or +10 D
The positive sign indicates that it is a converging or convex lens.
To calculate the power of lens B:-
The power of lens B, P = 1/FB(in meters)
P = 1/ -0.1
∴ P = −10 dioptre or −10 D
The negative sign indicates that it is a diverging or concave lens.
In a convex lens, when the object is placed between the pole and focus, the image formed is always virtual and magnified. On the other hand, a concave lens produces a virtual, erect but diminished image.
Here the object is placed 8 cm from the lens which is at a distance less than the focal length, i.e. less than 10 cm. Thus, the 8 cm position of the object placed in front of the convex lens will produce a virtual and magnified image. The diagram for the same is as shown below:
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