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प्रश्न
In the given figure the radius of curvature of the curved face in the planoconvex and the planoconcave lens is 15 cm each. The refractive index of the material of the lenses is 1.5. Find the final position of the image formed.
उत्तर
The focal length of the plano-convex lens is:
`1/f = (1.5 - 1)(1/((+10)) - 1/∞) = 1/20`
`f = 20`
The focal length of plano-concave lens is:
`1/f = (1.5 - 1)(1/∞ - 1/10) = -1/20`
`f = -20`
Since parallel beams are incident on the lens, its image from plano-concave lens will be formed at +30 cm from it (at the focus) and will act as an object for plano-concave lens. Since the two lenses are separated by a distance of 20 cm, therefore for the next lens.
u = +10 cm
`v = (uf)/((u + f)) = (10 xx(- 20))/(10 + (- 20)`
`v = (-200)/(-10)`
`v` = 20 cm (final position of the image formed)
संबंधित प्रश्न
A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is
- a convex lens of focal length 20 cm, and
- a concave lens of focal length 16 cm?
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A double convex lens of + 5 D is made of glass of refractive index 1.55 with both faces of equal radii of curvature. Find the value of its radius of curvature.
A convex lens forms a real image of a point object placed on its principals axis. If the upper half of the lens is painted black,
(a) the image will be shifted downward
(b) the image will be shifted upward
(c) the image will not be shifted
(d) the intensity of the image will decrease.
Answer the following question.
An optical instrument uses a lens of 100 D for the objective lens and 50 D for its eyepiece. When the tube length is kept at 20 cm, the final image is formed at infinity.
(a) Identify the optical instrument.
(b) Calculate the magnification produced by the instrument.
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