Magnification, power of lens, combination of thin lenses
- In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power (p) and magnification (m) for each lens will be, respectiv… Answer: 3. 4p and m⁴ Key idea: powers of thin lenses in contact add, while magnifications of successive images multiply. Power: P=p+p+p+p=4p... 1
- Two thin lenses are of same focal lengths (f), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be : Answer: 1. Infinite For lenses in contact, 1/F=dfrac1f₁+dfrac1f₂ . f₁=+f , f₂=-f : 1/F=1/f-1/f=0 , so F=∞ . The combination behaves like a p... 1
- In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)? Answer: 4. -100 cm Add the powers of the two refracting surfaces of the lens ( n=1.5 ) placed in a medium of index 1.6 , using P=n₂-n₁/R . S... 1
- A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is : Answer: 4. +5D Use the lens maker's formula: 1/f=(μ-1)(dfrac1R₁-dfrac1R₂) . For a biconvex lens R₁=+20 cm, R₂=-20 cm: 1/f=0.5(dfrac120+dfrac... 1
- A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm w… Answer: 2. 15 Key idea: a parallel beam stays parallel only if the lens separation makes the focal points coincide. The convex lens A focuse... 1
- Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F_1. When the space between the two lenses is filled with glycerin (which has the same refract… Answer: 2. 1 : 2 Two thin lenses in contact: dfrac1F₁=1/f+1/f , so F₁=f/2 . When the gap is filled with glycerin of the same index as glass,... 1
- Two identical glass (μ_g=3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water (μ_w=4/3). The focal length of the combination is Answer: 3. 3f/4 First find the radius of each lens, then the water lens, then combine powers. Glass lens: 1/f=(3/2-1)(2/R)=1/R , so R=f . Wa... 1
- A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be Answer: 1. concave, -0.25 diopter The person's far point is 400 cm; to see infinity the lens must form the image of a distant object at 400... 1
- Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]Column 1: (A) m = -2; (B) m = -1/2; (C) m = +2; (D) m = +1/2Column 2: (a) Convex mirror; (b) Concave mirror; (c) Real image; (d) Virtual i… Answer: 1. A → b and c; B → b and c; C → b and d; D → a and d Key idea: real images have negative m (inverted); virtual images have positive... 1