With a neat labelled diagram explain the formation of image in a simple microscope.

A simple magnifier or microscope is a converging lens of small focal length. If the object is at a distance slightly less than the focal length of the lens, the image is virtual and closer than infinity. The near point of the normal eye is 25 cm . i.e. it causes some strain on the eye. Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye. The linear magnification m for the image formed at the near point D by a simple microscope can be obtained by using the relation m = v u = v 1 v - 1 f = 1 - v f Now according to our sign convention, v is negative, and is equal in magnitude to D Thus, the magnification is m = 1 + D f We will now find the magnification when the image is at infinity. In this case we will have to obtain the angular magnification. Suppose the object has a height h . The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i.e. at a distance D . The angle subtended is then given by tan θ o = h D ≈ θ o The angle subtended at the eye by the image when the object is at u . From the relations h ' h = m = v u We have the angle subtended by the image, tan θ i = h ' - v = h - v v u = h - u ≈ θ i ⇒ θ i = h f (when u = - f ) Therefore, angular magnification is m = θ i θ o = D f .

Define focal length of a concave mirror. Prove that the radius of curvature of a concave mirror is double its focal length.

The focal length of a concave mirror is the distance between the Pole and the principal focus. Consider the following figure of a concave mirror. Let C be the centre of curvature of the mirror. Consider a ray parallel to the principal axis striking the mirror at M . Then CM will be perpendicular to the mirror at M . Let θ be the angle of incidence, and MD be the perpendicular from M on the principal axis. Then, ∠ M C P = θ Also, ∠ M F P = 2 θ Now, tan θ = MD CD and tan 2 θ = MD FD For small θ which is true for paraxial rays, tan θ = θ and tan 2 θ = 2 θ Therefore, MD FD = 2 MD CD ⇒ FD = DC 2 Now, for small θ , the point D is very close to the point P . Therefore, FD = f and CD = R That means, f = R 2

A small angled prism of 4 ° deviates a ray through 2 . 48 ° . Find the refractive Index of the prism.

It is given that the prism under consideration is a thin prism. Also, The angle of prism, A = 4 ° Angle of deviation, δ = 2 . 48 ° Let n be the refractive index of the prism. We know that for a thin prism, δ = A n - 1 ⇒ n = δ A + 1 ⇒ n = 1 . 62

A concave mirror produces an image of a long vertical pin, placed 40 cm from the mirror, at the position of the object. Find the focal length of the mirror (in cm ).

When an object is placed at the centre of curvature of a concave mirror, a real, inverted image of the same size as the object will form at the centre of curvature itself. This is illustrated in the figure. It is given in the question that image is formed at the same position as the object. This implies that the object is placed at the centre of curvature. That means, radius of curvature, R = - 40 cm Therefore, focal length, f = - 40 2 ⇒ f = - 20 cm

HARD

12th Andhra Pradesh Board

IMPORTANT

Earn 100

A ray of light is incident at an angle of $60 °$ on the face of a prism of angle $30 °$ . The emergent ray makes an angle of $30 °$ with the incident ray. Calculate the refractive index of the material of the prism.

Important Questions on Ray Optics and Optical Instruments

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 3

Two lenses of power

- 1.75 D

and

+ 2.25 D

respectively, are placed in contact. Calculate the focal length of the combination.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 4

Some rays falling on a converging lens are focussed

20 cm

from the lens. When a diverging lens is placed in contact with the converging lens, the rays are focussed

30 cm

from the combination. What is the focal length of the diverging lens?

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 5

A double convex lens of focal length

15 cm

is used as a magnifying glass in order to produce an erect image which is

3

times magnified. What is the distance between the object and the lens?

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 7

The distance between two point sources of light is

24 cm

. Where should you place a converging lens of focal length

9 cm

, so that the images of both sources are formed at the same point?

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 8

Find two positions of an object, placed In front of a concave mirror of focal length $15 cm$ , so that the Image formed is $3$ times the size of the object.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 9

When using a concave mirror, the magnification is found to be $4$ times as much when the object is $25 cm$ from the mirror as it is with the object at $40 cm$ from the mirror, the image being real in each case. What Is the focal length of the mirror?

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 2.1

A small candle,

2.5 c m

in size is placed at

27 c m

in front of a concave mirror of radius of curvature

36 c m

. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 2 - Ray Optics and Optical Instruments>MODEL QUESTIONS (IPE PATTERN)>Q 2.2

4.5 c m

needle is placed

12 c m

away from a convex mirror of focal length

15 c m

. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

A ray of light is incident at an angle of 60° on the face of a prism of angle 30°. The emergent ray makes an angle of 30° with the incident ray. Calculate the refractive index of the material of the prism.

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !

A ray of light is incident at an angle of $60 °$ on the face of a prism of angle $30 °$ . The emergent ray makes an angle of $30 °$ with the incident ray. Calculate the refractive index of the material of the prism.