Advertisements
Advertisements
Question
A card sheet divided into squares each of size 1 mm2 is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm) held close to the eye.
- What is the magnification produced by the lens? How much is the area of each square in the virtual image?
- What is the angular magnification (magnifying power) of the lens?
- Is the magnification in (a) equal to the magnifying power in (b)? Explain.
Advertisements
Solution
(a) For magnification by the magnifying lens.
Let us use lens formula,
u = −9 cm, f = +9 cm
`1/"v" - 1/"u" = 1/"f"`
`1/"v" - 1/(-9) = 1/9`
`1/"v" = 1/9 - 1/9` = 0
Image position v = ∞
Magnification, `"m" = "v"/"u"` = ∞
A large image will be formed.
(b) Angular magnification, m = `"D"/"u" = 25/9` = 2.8
(c) No, the linear magnification by a lens and the magnifying power (angular magnification) of a magnifying glass have different values.
The linear magnification is calculated using m = `"v"/"u"`, whereas angular magnification is m = `"D"/"u" = β/α`, the ratio of the angle subtended by the image of the object at eye lens 'β' to the angle subtended by the object assumed to be at least distance at eye lens 'α'.
The linear magnification and angular magnification in a microscope have similar magnitude when the image is at least a distance of distinct vision, i.e., 25 cm.
RELATED QUESTIONS
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?
An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?
A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm.
(a) What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
(b) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?
Two concave lenses L1 and L2 are kept in contact with each other. If the space between the two lenses is filled with a material of smaller refractive index, the magnitude of the focal length of the combination
Two converging lenses of unequal focal lengths can be used to reduce the aperture of a parallel beam of light without loosing the energy of the light. This increase the intensity. Describe how the converging lenses should be placed to do this.
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 ______.
Will the focal length of a lens for red light be more, same or less than that for blue light?
An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?
The straight line passing through the optical centre and the centres of curvature of the lens surfaces is called the:
Which of the following correctly represents the Lens Maker's Formula?
In the Lens Maker's Formula, the symbols \[R_1\] and \[R_2\] denote:
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 concave lens is:
A ray parallel to the principal axis, after refraction through a concave lens, appears to diverge from:
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:
If the refractive index of a liquid equals that of a glass lens (\[n_1 = n_2\]), the lens maker relation gives \[\frac{1}{f} = 0\]. This means the focal length of the lens becomes:
A concave lens is used in spectacles for myopia because it:
