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The power of a convex lens is +2.5 D. What is its focal length?
Power $P = 1/f$. Given $P = +2.5 D$. Therefore, $f = 1/2.5 = 0.4 m = 40 cm$. 'The power of a lens is positive for a converging lens...Thus, when an optician prescribes a corrective lens of power + 2.5 D, the required lens is a convex lens of focal length + 40 cm.'
A concave lens has a power of -4.0 D. What is its focal length?
Power $P = 1/f$. Given $P = -4.0 D$. Therefore, $f = 1/(-4.0) = -0.25 m = -25 cm$. 'A lens of power of – 4.0 D means a concave lens of focal length – 25 cm.'
Which of the following statements about the power of a lens is INCORRECT?
Power $P = 1/f$. Therefore, a shorter focal length implies a higher power. 'Clearly, a lens of shorter focal length bends the incident light more... The power P of a lens is defined as P = 1/f.'
Two thin lenses of focal lengths $f_1$ and $f_2$ are placed in contact. The effective focal length $f$ of the combination is given by:
For thin lenses in contact, the reciprocal of the effective focal length is the sum of the reciprocals of individual focal lengths. 'If several thin lenses of focal length $f_1, f_2, f_3,...$ are in contact, the effective focal length of their combination is given by $1/f = 1/f_1 + 1/f_2 + 1/f_3 + …$'
If two thin lenses with powers $P_1$ and $P_2$ are placed in contact, the net power $P$ of the combination is:
The net power of a combination of thin lenses in contact is the algebraic sum of their individual powers. 'In terms of power, Eq. (9.31) can be written as $P = P_1 + P_2 + P_3 + …$'.
A convex lens of focal length 10 cm is placed in contact with a concave lens of focal length 30 cm. What is the power of the combination?
For the convex lens, $f_1 = +10 cm = +0.1 m$, so $P_1 = 1/f_1 = 1/0.1 = +10 D$. For the concave lens, $f_2 = -30 cm = -0.3 m$, so $P_2 = 1/f_2 = 1/(-0.3) = -3.33 D$. The net power $P = P_1 + P_2 = +10 D - 3.33 D = +6.67 D$. 'The sum in Eq. (9.32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses).'
If the total magnification of a combination of lenses is $m$, and the individual magnifications are $m_1, m_2, m_3,...$, then:
The total magnification of a combination of lenses is the product of the individual magnifications. 'The total magnification m of the combination is a product of magnification ($m_1, m_2, m_3,...$) of individual lenses $m = m_1 m_2 m_3 ...$'
A system of combined lenses is often used in optical instruments to achieve:
Combination of lenses helps to obtain diverging or converging lenses of desired magnification. It also enhances sharpness of the image. Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments.
Which of the following optical instruments commonly uses a system of combined lenses?
Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments.
When referring to the power of a lens, what does 1 Dioptre (D) signify?
The SI unit for power of a lens is dioptre (D): 1D = 1m–1. The power of a lens of focal length of 1 metre is one dioptre.
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