A slide projector has to project a 35 mm slide ( 35 mm × 23 mm ) on a 2 m × 2 m screen at a distance 10 m from the lens. What should be the focal length of the lens in the projector?

The dimensions of the slide = 35 mm × 23 mm . The distance of the screen from the lens, v = + 10 m . The dimension of the screen is 2 m × 2 m . Since the image is obtained on the screen, it is a real image. 35 mm slide is magnified to 2 m . Hence, the magnification m = - 2 m 35 mm = - 2000 mm 35 mm = - 400 7 . The negative sign indicates that a real and inverted image is formed. The lateral magnification for the lens is, m = v u , where, v is the distance of the image from the lens and u is the distance of the object from the lens. ⇒ - 400 7 = + 10 m u ⇒ u = - 7 40 m . From the lens equation, 1 f = 1 v - 1 u ⇒ 1 f = 1 10 - 1 - 7 40 = 1 10 + 40 7 . Therefore, the focal length of the lens in the projector, f = 0 . 172 m = 17 . 2 cm .

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HOW IS lens magnification calculated?

Important Questions on Refraction at Spherical Surface and Spherical Lens

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

For which position of the object, magnification of convex lens is -1 (minus one)?

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

An object approaches a convergent lens from the left of the lens with a uniform speed

10 m / s

and stops at the focus. The image moves

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

An extended object is placed at point $O$ , $10 cm$ in front of a convex lens $L_{1}$ and a concave lens $L_{2}$ is placed $10 cm$ behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are $20 cm$ . The refractive index of both the lenses is $1.5$ . The total magnification of this lens system is:

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

Use the lens equation and prove that for a convex lens when the object is placed within the focal length, the image will be virtual.

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

Where should an object be placed on the axis of a convex lens of focal length

8 cm

so as to achieve magnification of

- 4

? (Distances are measured from optic centre of the lens)

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

An object is moving with a velocity of

0.01 {m s}^{- 1}

towards a convex lens of focal length

0.3 m

. The magnitude of the rate of separation of an image from the lens when the object is at a distance of

0.4 m

from the lens is

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A screen is placed

90 cm

from an object. The image is formed by using a convex lens twice on the screen by putting the lens at two different locations separated by

20 cm .

The focal length of the lens is approximately equal to:

MEDIUM

Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A convex lens of focal length

f

is placed some where in between an object and a screen. The distance between object and screen is

x

. If numerical value of magnification produced by lens is

m

, focal length of lens is

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A lens forms real and virtual images of an object when the object is at

u_{1}

and

u_{2}

distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (Take the magnification of the real image as

' m'

)

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A point object is placed on the axis of a thin convex lens of focal length $0.05 m$ at a distance of $0.2 m$ from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of $A cm$ , then what is the amplitude of oscillation of the image?

[you may assume, $\frac{1}{1 + x} \approx 1 - x,$ where $x ≪ 1]$

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

An object approaches a convergent lens from the left of the lens with a uniform speed

5 m s^{- 1}

and stops at the focus, the image

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A convex lens of focal length

25 cm

produces images of the same magnification

2

, when an object is kept at two positions

x_{1}

and

x_{2}

(x_{1} > x_{2})

from the lens. The ratio of

x_{2}

and

x_{1}

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A converging lens of focal length 20 cm and diameter 5 cm is cut along the line AB. The part of the lens shown shaded in the diagram is now used to form an image of a point P placed 30 cm away from it on the line XY. Which is perpendicular to the plane of the lens. The image of P will be formed.

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes from $m_{25} t o m_{50} .$ The ration $\frac{m_{25}}{m_{50}}$ is

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A slide projector has to project a

35 mm

slide

(35 mm \times 23 mm)

on a

(2 m \times 2 m)

screen at a distance

10 m

from the lens. What should be the focal length of the lens in the projector?

HARD

Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A convex lens produces a double sized real image when an object is placed at a distance of

18 cm

from it. Where should the object be placed to produce a triple sized real image?

MEDIUM

Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A convex lens is placed between object and a screen. The size of object is 3 cm and an image of height 9 cm is obtained on the screen. When the lens is displaced to a new position, what will be the size of image on the screen?

MEDIUM

Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A converging lens has a focal length of

0.12 m .

To get an image of unit magnification the object should be placed at what distance from the converging lens?

HARD

Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A pin of length

2.00 cm

is placed perpendicular to the principal axis of a converging lens. An inverted image of size

1.00 cm

is formed at a distance of

40.0 cm

from the pin. Find the focal length of the lens and its distance from the pin.

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Physics>Optics>Refraction at Spherical Surface and Spherical Lens>Linear and Longitudinal Magnification

A convex lens forms an object on a screen. The height of the image is 9 cm. The lens is now displaced until an image is again obtained on the screen. The height of this image is 4 cm. The distance between the object and the screen is 90 cm.

HOW IS lens magnification calculated?

Important Questions on Refraction at Spherical Surface and Spherical Lens

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