### Ray Optics and Optical Instruments

1. a) Define Snells' law. Using a neat labelled diagram derive an expression for the refractive index of the material of an equilateral prism.

b) A ray of light, after passing through a medium, meets the surface separating the medium from air at an angle of 45° and is just not refracted. What is the refractive index of the medium?

A: Snell's Law:

1) The incident ray, the refracted ray and the normal to the interface at the point of incidence lie in same plane.

2) The ratio of sine of angle of incidence (i) to the sine of angle of refraction (r) is constant.

Where n21 is a constant and is called refractive index of the second medium with respect to the first medium.

Expression for refractive index of a prism:

Let us suppose that ABC is a glass prism.

A = Refracting angle of the prism

n21 = Refractive index of glass w.r. to air

PQ = Incident ray.

QR = Refracted ray in the prism

RS = Emergent ray

The normal to AB and AC meet at N.

i = Angle of incidence at the first surface

r1 = Angle of refraction at the first surface

r2 = Angle of refraction at the second surface (if light enters 2nd surface)

e = Angle of Emergence

δ = Angle of deviation (Angle between PQ and RS)

The total deviation δ = Sum of deviations at the two faces.

δ = (i - r1) + (e - r2)

or

δ = i + e - (r1 + r2)   (4)

Substituting Equation (3) in this,

δ = i + e - A    (5)

This shows that the angle of deviation, δ depends on angle of incidence, i. The graph between i and δ (i - δ curve) is a Parabola as shown in the figure. The value of δ decreases to a minimum called angle of minimum deviation (Dm) and then increases.

At δ = Dm = angle of minimum deviation, it was found experimentally that

i = e and r1 = r2 = r

Putting these in equations (3) and (5),

This is equation for angle of incidence in terms of angle of the prism and angle of minimum deviation.

When the light ray is passing from medium 1 (air) to medium 2 (glass), the refractive index of medium 2 with respect to medium 1 is given by

(b)

A: Ray is not just refracted

Hence, the angle given is critical angle

ic = 45°, n21 = ?

Critical angle formula: n21 = sin ic

Refractive index of the medium is 1.414

2. Draw a neat labelled diagram of a compound microscope and explain its working. Deduce an expression for its magnification.

A: Compound Microscope: Compound microscope consists of two convex lenses. The lens facing the object is called objective. The lens facing the eye is called Eyepiece.

Working: The ray diagram of compound microscope is as shown in the figure.

The object AB is outside its focus of objective.

Hence, it forms a real, inverted and magnified image A'B' just inside the focus of eyepiece. Then the eye piece acts as a simple microscope and forms a final image A"B" at the distance of near point (D). The final image A"B" is virtual, well magnified and inverted.

Expression for magnification of compound Microscope: The Magnification of Compound Microscope (M) is equal to product of magnifications of its objective (mo) and eye piece (me)

m = mo .me   (1)

Magnification of objective: As the image formed is real, the ratio of size of image to size of object is magnification.

Where 'L' is distance between the foci of objective and eyepiece. As fo and fe are very small, L can be taken as distance between the objective and the eyepiece.

Magnification of Eyepiece:

Eyepiece acts as simple microscope.

Where L is distance between objective and eyepiece.

D is distance of near point,

fo = focal length of objective and

fe = focal length of eyepiece

3. a) Using a neat labelled diagram derive the mirror equation. Derive linear magnification.

b) An object is placed at 5 cm from a convex lens of focal length 15 cm. What is the position and nature of the image?

A: Derivation of mirror equation:

Consider a concave mirror. P is its pole. F is its Focus. C is its centre of curvature. AB is an object infront of the mirror. A'B' is its image formed by the mirror.

PF = f = focal length of concave mirror

PB' = v = image distance

PB = u = object distance

In figure, the triangles A'B'F, MPF are similar triangles. Hence, the ratio of their corresponding side will be equal.

The ttriangles A'B'P, ABP are also similar triangles. Hence, the ratio of their corresponding sides will be equal.

From sign convention distances from P against the direction of incident light are negative.

B'P = -v, FP = -f, BP = -u

Putting these in equation (3), we get

This is called mirror formula

Linear Maginfication: The ratio of height of the image (h') to height of the object (h) is called linear Magnification (m).

(b)

A: u = -5 cm ; f = +15 cm, v = ?

The nature of image is virtual because of (-) sign of v.

4. Obtain an expression for the combined focal length for two this convex lenses kept in contact & hence obtain an expression for the combined power of the combination of the lenses?

A: Combined Focal Length of two thin lenses in contact

Consider two thin convex lenses A, B kept in contact. Their focal lengths are f1, frespectively. O is the point object. For our convenience, if only lens A is there, the image of O could be I1. Now I1 acts as virtual object for the lens B which forms the image I. Object distance is u. Image distance of I is v and image distance of I1 is v1

Applying thin less formula to the first lens A, we get

This is the equation for combined focal length (f), of two thin convex lenses kept in contact.

Expression for combined power:

As per the defination of power of a lens,

P = P1 + P2

This is expression for combined power (P) of two thin convex lenses of powers (P1, P2) kept in contact.

1. Define critical angle. Explain total internal reflection using a neat diagram.

A: Critical Angle: When a light ray is passing from denser medium to rarer medium, the angle of incidence in denser medium for which the angle of refraction becomes 90° in rarer.

Equation for critical angle is

sin ic = n21

Where n21 = refractive index of the denser medium with respect to rarer medium.

Total Internal Reflection: When a light ray is passing from denser medium to rarer medium if the angle of incidence is greater than its critical angle (i > ic), it gets reflected into the same denser medium without any refraction. This phenomenon is called total internal reflection.
In figure, total internal reflection taken place at the point O4.

An optical fiber works on the principle of total internal reflection.

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

A: Simple Microscope: A simple Microscope consists of only one convex lens of small focal length. It is also called as magnifying glass.

In this the object is placed between the principal focus F and the optic centre of the convex lens.

Formation of image can be explained by two ray diagram. The light ray coming from the object parallel to principal axis refracts at lens and passes through second principal focus F'. Another light ray from the object passes through the optic centre of the lens undeviated. These two rays meet on the back side of the object to form the image. Hence, the image formed is virtual, erect and magnified as shown in the figure. The closest comfortable distance for viewing the image is the distance of the near point D = 25 cm.

3. Explain the formation of a mirage.

A: Mirage: An optical phenomenon in which light rays are bent to produce a displaced image of distant object is called mirage.

Mirages are formed due to total internal reflection of light at air of less density in lower levels on hot summer days. When the ground is too hot, the air in lower levels gets heated and its density decreases. As a result, its refractive index and optical density decreases. That means, on hot summer days, rarer medium (air of less refractive index) is formed at lower levels and denser medium (air of higher refractive index) remains at higher levels. Now the light rays coming from denser medium to rarer medium and satisfy the condition, i > ic and hence total internal reflection takes place. As a result an observer gets an impression that reflection of distant objects is occuring due to presence of water. But water will not be there. It is an optical illusion called mirage.

4. Explain the cartesian sign convention for mirrors

A: Cartesian sign convention: The following cartesian sign convention is used for measuring various distances in the ray diagrams of spherical mirrors:

1) Object is always placed to the left of mirror.

2) All distnaces are measured from the pole of the mirror.

3) Distances measured in the direction opposite to that of the incident ray are negative.

4) Distances measured along Y-axis above the principal axis below the principal axis are negative.

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

A: Focal Length (f): The distance between the focus F and the pole P of the concave mirror is called focal length (f) of the concave mirror.

To Show that R = 2f for concave mirror:

Consider a concave mirror of pole P, focus F and centre of curvature C. When a light ray parallel to its principal axis is incident at M, the reflected ray passes through its focus F. The line joining M and C is normal to the mirror at M.

The perpendicular drawn from M on to principal axis is MD.

As θ is very small,

tan θ = θ and tan 2θ = 2θ

As D is very close top,

DC = PC = R = Radius of curvature

and DF = PF = f = Focal length

Radius of curvature = 2 Focal length

6. Explain the formation of rainbow.

A: Rainbow: The multicoloured arc that appears in the sky, opposite to sun on a rainy day is called rainbow. Rainbow is the combined effect of dispersion, refraction and total internal reflection of sunlight by spherical water droplets of rain in atmosphere. The water drops in atmosphere acts as small prisms and cause dispersion and total internal reflection of sunlight to form rainbow.

The primary rainbow is a 3 step process:

1) Sunlight is first refracted as it enters a raindrop, which causes different colours.

2) These refracted rays strike the inner surface of the drop and get internally reflected because their angle of incidence (i) is greater its critical angle (ic).

3) These internally reflected rays again get refracted at the opposite surface and come out.

As Red is less deviated, red from upper level drops comes straight to observer and appears on top. As violet is deviated more, it comes from lower level drops and appears at bottom.

The secondary rainbow is also formed due to double internal reflection of sunlight in the rain drops. This appears faint and the colours in it will be in reverse order.

7. Why does the setting sun appeared Red?

A: Sunset appeared Red: Sunlight passes through the atmosphere before it reaches us. Sun light is composed of seven colours (VIBGYOR). In the evenings, when the sun is near the horizon, the rays have to travel longer path in the atmosphere to reach us. The dust, smoke and water vapour present in the atmosphere scatter away these colours differently depending on their wavelengths. Scattering is more if wavelength is less. As red has longer wavelength, it scatters less. Thus red comes to us straight while other colours get scattered into space. That is why, setting sun appeared red.

1. Define focal length and radius of curvature of a concave lens.

A: Focal Length (f): The distance between the optic centre of concave lens and its principal focus (f) is called focal length (f) of the concave lens.

Radius of curvature(R): The linear distance between pole and centre of curvature is called radius of curvature.

2. What is optical density and how is it different from mass density?

A: Optical density: The property of a medium to slow down the speed of light is called optical density. A medium of heigher refractive index has more optical density. Water is denser compared to air (rarer).

Mass density: Mass per unit volume of a substance is called mass density. There is no direct relation between mass density and optical density. A medium of less mass density may have less or more optical density.

3. Define 'Power' of a convex lens. What is its units?

A: Power of convex lens: The tangent of angle by which a convex lens converges a beam of light, of unit breadth at its optic centre, to its focus is called power of the convex lens (P).

Power of a lens is equal to reciprocal of its focal length (f).

Unit: The SI unit of power of a lens is Dioptre. Its simbol is D.

4. A small angled prism of 4° deviates a ray through 2.48°. Find the refractive index of the prism.

A: A = 4°, Dm = 2.48, n21 = ?

Formula: For a thin angled Prism,

Dm = (n21 - 1)A

2.48 = (n21 - 1) 4

n21 = 1.62

5. What is 'dispersion'? Which colour gets relatively more dispersed?

A: When a composite beam of light passes through a prism, it splits up into its constituent colours. This phenomenon is called dispersion of light. Dispersion of white light gives VIBGYOR colours. The violet colour with less wavelength disperses (deviates) more

6. What is myopia? How can it be corrected?

A: Myopia or near sightedness: The optical defect of human eye in which the light from a distant object is converged to a point in front of the retina and not on to the retina is called myopia or near sightedness. It is caused due to too much convergence of light rays by the eye lens.

7. What is hypermetropia? How can it be corrected?

A: Hypermetropia (or) Farsightedness: The optical defect of human eye in which the incoming light from an object is converged to a point behind the retina and not on to the retina is called hypermetropia or farsightedness. It is cause due to less convergence of light rays by the lens.

Posted Date : 27-08-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.

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