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. 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? - Physics


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?



(a) Focal length of the magnifying glass, f = 5 cm

Least distance of distance vision, d = 25 cm

Closest object distance = u

Image distance, v = −d = −25 cm

According to the lens formula, we have:

`1/f = 1/v - 1/u`

`1/u = 1/v - 1/f`

`= 1/-25 - 1/5 = (-5-1)/25 = -6/25`

`:. u = -25/6 = -4.167  cm`

Hence, the closest distance at which the person can read the book is 4.167 cm.

For the object at the farthest distant (u’), the image distance `(v') = oo`

According to the lens formula, we have:

`1/f =1/"v'"  - 1/"u'"`

`1/"u'" =1/oo  - 1/5 = -1/5`

`:. "u'" = -5 cm`

Hence, the farthest distance at which the person can read the book is 
5 cm.

(b) Maximum angular magnification is given by the relation:

`alpha_"max" = d/|u|`

`= 25/ (25/6) = 6`

Minimum angular magnification is given by the relation:

`alpha_"min" = d/|u'|`

`= 25/5 = 5`

Concept: Refraction at Spherical Surfaces and Lenses - Refraction by a Lens
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Chapter 9: Ray Optics and Optical Instruments - Exercise [Page 348]


NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 28 | Page 348


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) a convex lens of focal length 20 cm, and (b) 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 screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.

An object 1.5 cm in size is placed on the side of the convex lens in the arrangement (a) above. The distance between the object and the convex lens is 40 cm. Determine the magnification produced by the two-lens system, and the size of the image

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.

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.

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.

A small piece of wood is floating on the surface of a 2.5 m deep lake. Where does the shadow form on the bottom when the sum is just setting? Refractive index of water = 4/3.

A pin of length 2.0 cm lies along the principal axis of a converging lens, the centre being at a distance of 11 cm from the lens. The focal length of the lens is 6 cm. Find the size of the image.

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?

In many experimental set-ups the source and screen are fixed at a distance say D and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.

A plano convex lens has diameter of 10 cm and its thickness at the centre is 0.5 cm. Speed of light in the lens is 2 × 108 ms-1. What is the focal length of the lens?


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