Advertisements
Advertisements
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?
Advertisements
उत्तर
In the given situation, the object is virtual and the image formed is real.
Object distance, u = +12 cm
(a) Focal length of the convex lens, f = 20 cm
Image distance = v
According to the lens formula, we have the relation:
`1/"v" - 1/"u" = 1/"f"`
`1/"v" - 1/12 = 1/20`
`1/"v" = 1/20 + 1/12`
`1/"v" = (3 + 5)/60`
`1/"v" = 8/60`
v = `60/8`
∴ v = 7.5 cm
Hence, the image is formed 7.5 cm away from the lens, towards its right.
(b) Focal length of the concave lens, f = −16 cm
Image distance = v
According to the lens formula, we have the relation:
`1/"v" - 1/"u" = 1/"f"`
`1/"v" = 1/"f" + 1/"u"`
`1/"v" = 1/-16 + 1/12`
`1/"v" = (-3 + 4)/48`
`1/"v" = 1/48`
∴ v = 48 cm
Hence, the image is formed 48 cm away from the lens, towards its right.
संबंधित प्रश्न
The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3 m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?
Figure shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?
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.
An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The image ______.
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.
Show that the least possible distance between an object and its real image in a convex lens is 4f, where f is the focal length of the lens.
The straight line passing through the optical centre and the centres of curvature of the lens surfaces is called the:
The point near the centre of a thin lens through which a ray of light passes without appreciable deviation is called the:
The point on the principal axis where rays parallel to the principal axis actually meet after refraction, or appear to diverge after refraction, is called the:
Which of the following correctly represents the Lens Maker's Formula?
Which of the following is the correct Thin Lens Formula?
For a thin lens, the magnification \[m\] in terms of image distance \[v\] and object distance \[u\] is given by:
According to the new Cartesian sign convention for lenses, the focal length of a convex lens is:
According to the new Cartesian sign convention, all distances in lens problems are measured from:
A ray of light passing through the optical centre of a thin lens:
A ray directed towards the principal focus of a concave lens, after refraction, emerges:
Using the sign convention with \[OB = -u\] and \[DI = +v\] in the combined refraction equation for a thin lens gives:
A lens with an infinite focal length behaves like:
