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Question
Define power of a lens. Write its units. Deduce the relation `1/f =1/f_1 +1/f_2`for two thin lenses kept in contact coaxially.
Solution
Consider two lenses A and B of focal length f1 and f2 placed in contact with each other. An object is placed at a point O beyond the focus of the first lens A. The first lens produces an image at I1 (real image), which serves as a virtual object for the second lens B, producing the final image at I.
Since the lenses are thin, we assume the optical centers (P) of the lenses to be co-incident. For the image formed by the first lens A, we obtain
`1/v_1 -1/u =1/f_1 ........ (1)`
For the image formed by the second lens B, we obtain
`1/v -1/v_1 =1/f_2 ........ (2)`
Adding equations (1) and (2), we obtain
`1/v -1/u =1/f_1 + 1/f_2 ........ (3)`
If the two lens system is regarded as equivalent to a single lens of focal length f, we have
`1/v -1/u =1/f_1 ........ (4)`
From equations (3) and (4), we obtain
`1/f_1 + 1/f_2 =1/f_1 `
RELATED QUESTIONS
A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.
Consider two statements A and B given below:
A: real image is always inverted
B: virtual image is always erect
Out of these two statements:
What is the nature of a lens having a power of + 0.5 D?
What is the nature of a lens whose power is, −4 D?
A lens has a focal length of, −10 cm. What is the power of the lens and what is its nature?
Two lenses A and B have focal lengths of +20 cm and, −10 cm, respectively.
(a) What is the nature of lens A and lens B?
(b) What is the power of lens A and lens B?
(c) What is the power of combination if lenses A and B are held close together?
A pin of length 2.00 cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1.00 cm is formed at a distance of 40.0 cm from the pin. Find the focal length of the lens and its distance from the pin.
Surabhi from std. X uses spectacle. The power of the lenses in her spectacle is 0.5 D.
Answer the following questions from the given information:
- Identify the type of lenses used in her spectacle.
- Identify the defect of vision Surabhi is suffering from.
- Find the focal length of the lenses used in her spectacle.
The power of the magnifying glass depends on the distance of the magnifying glass from object.
Assertion and reasoning type
- Assertion: Myopia is due to the increase in the converging power of eye lens.
- Reason: Myopia can be corrected with the help of concave lens.
