Unit 6bc tủ tài liệu training

Explain the working of a convex lens of short focal length as a simple microscope.. b how will its resolving power be affected when i the frequency of light used to illuminate the object

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VERY SHORT AND SHORT-ANSWERS QUESTIONS

81 A lens placed in a medium behaves as an ordinary glass plate What is the refractive index of the

medium relative to that of the lens ?

82 A ray of light, after refraction through a concave lens, emerges parallal to the principal axis.

Under what conditions does this happen ?

83 The focal length of a biconvex lens is half the radius of curvature of either face Calculate the

refractive index of the material of the lens

84 What is the inclination of the refracted ray inside the prism with the base of the prism, if the

prism is set in the position of minimum deviation ?

85 When a beam of white light is passed through a prism, the deviation suffered by violet colour is

more than that suffered by red colour Why ?

86 Write the names of the three main components of a spectrometer.

87 What is the function of the collimator in a spectrometer ?

88 Why is red coloured light used in danger signals or traffic stops ?

89 Why is the sequence of colours in the secondary rainbow reverse of that in the primary rainbow ?

90 Why do we prefer a magnifying glass of short focal length ?

91 An object is seen through a microscope first in red light and then in violet light In which case is

the magnification larger ?

92 How can you increase the resolving power of a telescope ?

93 The focal length of a convex lens is 25 cm Where should the object be placed in front of the lens

so as to get a real image equal to the size of the object ?

94 The power of a lens is + 4D What is the nature and focal length of the lens ?

95. Two lenses of powers + 8D and + 4D are kept in contact, what is the focal length of thecombination ?

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1Prove the relation µ =

µ

a b

b a

96.

97 What is meant by apparent depth ? Derive a relation between apparent depth, real depth and

refractive index for near normal incidence

98 How do optical fibres transmit light without significant absorption ? Mention one practical

99 Derive the relation 1 2 2– 1

–

for refraction at a spherical surface The symbols have their usual meaning

100 Derive the thin lens formula (equation).

101 Derive the lens maker’s formula in the case of a double convex lens.

102 Define linear magnification produced by a lens Derive an expression for it.

103 Show that the refractive index of the material of a prism is given by

+ δ

= where the symbols have their usual meanings.

104 Derive the expression for the angle of deviation for a ray of light passing through an equilateral

105 What is angular dispersion ? Derive an expression for the angular dispersion produced by a

small angled prism for small angles of incidence

106 What is emission spectrum ? Distinguish between the three types of emission spectra.

107 Explain the working of a convex lens of short focal length as a simple microscope.

OR

Explain the working of a simple microscope and show that its magnification is given by

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= 1 +D

m

f where f is the focal length and D is the least distance of distinct vision. (AISSCE 1992)

108. With the help of a ray diagram explain the working principle of a compound microscope

(AISSCE 1993)

109. Draw a labelled diagram of an astronomical telescope forming the final image at the near point.Write down the formula for its magnifying power (AISSCE 1993)

110. Draw a labelled diagram of a telescope and explain its working when the final image is formed

at infinity Give an expression for its magnifying power

(AISSCE 1992, AISSCE Delhi 1999)

111. Write two common applications of simple microscope (magnifying glass)

112. Which one has higher refractive index - crown glass or flint glass ?

113. What would be the colour of the sky if viewed from the moon ?

114. (a) Draw a labelled ray diagram for a refracting type astronomical telescope (b) How will its magnifying power be affected on increasing for its eye piece (i) the focal length (ii) the

115. (a) Draw a labelled ray diagram for a compound microscope (b) how will its resolving power

be affected when (i) the frequency of light used to illuminate the object is increased, and (ii) the

focal length of the objective is increased (AISSCE 1997)

116. Draw a labelled ray diagram for a reflecting type telescope Write four advantages of a ing type telescope over a refracting type telescope? (AISSCE 1999)

reflect-117. How does (i) the magnifying power (ii) the resolving power of a telescope change on

increas-ing the diameter of its objective ? Give reasons for your answer (AISSCE 1998)

118. Violet light is incident on a converging lens of focal length f State, with reason, how the focal

length of the lens will change if the violet light is replaced by red light (AISSCE - 1999)

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119. A convex lens, made of a material of refractive index µ1,is kept in a medium of refractive index

µ2 Parallal rays of light are incident on the lens Complete the path of the rays of light

emerg-ing from the convex lens if (i) µ1> µ2 (ii) µ1= µ2 (iii) µ1< µ2 (AISSCE - 2000)

120 A concave lens, made of a material of refractive index µ1, is kept in a medium of refractiveindex µ2 A parallal beam of light is incident on the lens Complete the path of the rays of light

emerging from the concave lens if (i) µ1> µ2 (ii) µ1=µ2(iii) µ1< µ2 (AISSCE - 2000)

ANSWERS

81. One

82. When the incident ray is directed towards the principal focus of the

lens, then after refraction it emerges out parallal to the principal

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84. The refracted ray inside the prism is parallal to the base of the prism

85 We know that more the refractive index of the prism for a colour, more is the deviation Since

µ V > µR, violet colour suffers larger deviation than red

86. The three main components of a spectrometer are (i) collimator, (ii) prism table, and (iii) telescope.

87. The function of the collimator is to produce a beam of parallal rays

88. Red colour, being of the largest wavelength in the visible spectrum, scatters least Therefore, itcan easily be seen from large distances, even in foggy conditions

89. The sequence of colours in the secondary rainbow is reverse of that in the primary rainbowbecause it is formed by two internal reflections of light in water droplets, whereas primaryrainbow is formed by one internal reflection

90. The magnifying power of magnifying glass is given by m 1 D

93. To have a real image equal to the size of object, the object must be placed at a distance 2f from

the lens, i.e., at 2 × 25 = 50 cm from the lens.

m4

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95. Total power P = P1 + P2 = 8 + 4 = 12 D

12100

12

f P

a b

i r

On reversing the path, light travels from medium b to medium a Now the angle of incidence is

r and the angle of refraction is i Therefore the refractive index of the medium a w.r.t medium

b is

sin

µ = (2)sin

b a

r i

Medium a i

Fig 6 B.7

r

Medium b

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Eqs (1) and (2) give

1

µ = µ

a b

b a

97. The depth of an object lying in or below an optically denser medium appears to be less than its

real depth This is called the apparent depth.

r

Q

C P

A

I

B Medium a

Medium b O

i

Fig 6 B.8

In the figure (O) is a point object below a transparent slab Ray OA strikes the surface normally and moves undeviated Another ray OB strikes at B at an angle of incidence i and is refracted along BC The two refracted rays appear to diverge from I So I is the virtual image of O AI is the apparent depth and AO is the real depth.

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sin

sinsin

=

=

∠ AOB=∠ OBQ = i (alternate angles)

∠ AIB =∠ PBC = r (corresponding angles)

In the right triangles AOB and AIB

sini AB and sinr AB

98. Optical fibres consist of thousands of long fine quality glass or quartz fibres of high refractiveindex of about 1.7 They are coated with a material of refractive index 1.5 The thickness of eachfibre (strand) is about 10–4 cm

When light is incident on one end of the fibre at a small angle, it passes through the fibre suchthat it suffers total internal reflection along the fibre and finally comes out at the other end

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99. In Fig 6 B.9 XY is a convex refracting surface separating media 1 and 2 O is a point object on the principal axis OA is an incident ray which is refracted along AI i is the angle of incidence and r is the anlge of refraction Another ray OP strikes normally and goes without any devia- tion The two rays meet at I, so I is the image of O.

Let ∠AOP = α, ∠ AIP = β and ∠ ACP = γ

From Snell’s law

C P

A

β

X N

Y

Medium '1'

Medium '2' O

2

1 2 1

sin µ

µsin µ

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–

100 Let a linear object AB be placed in front of a convex lens of focal length f at a distance greater

than the focal length f of the lens Ray BP goes parallal to the principal axis and strikes the lens

at P After refraction it passes through the principal focus F Another ray passes through the

optical centre and moves undeviated The two refracted rays intersect at B′, so B′ is the image

of B In the same way, image of every point on AB is formed on A B′ ′ So A B′ ′ is the image of

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F A

A'

B' O

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–

=–

v u f This is the lens formula (equation).

101 Consider a convex lens of refractive index µ2placed in a medium of refractive index µ1 (< µ2)

[Fig 6 B.11] Let O be a point object, lying on the principal axis of the lens I1 is the image of

O formed by the spherical surface XP1Y Using the relation for refraction at a spherical surface,

where u is the distance of the object from C, v1 is the distance of the image I1 from C and R1 is

radius of curvature of the face XP1 Y.

Now we consider the refraction at face XP2 Y For this face, AB is the incident ray, which is refracted along BI Here I1 acts as a virtual object whose real image is formed at I In this case

the ray is passing from a denser to a rarer medium So we have

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where R2 is the radius of curvature of the face XP2 Y and v is the distance of the final image from C.

Adding Eq (1) and (2)

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Fig 6 B.11

B A X

′

=

In the figure, AB is a linear object placed on the principal axis of a lens A B′ ′ is the image of

AB formed by refraction through the lens.

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B

y

P

F A

A'

y'

B' C

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103 In the figure, a ray of light PQ strikes the refracting face AB of the prism at Q It is refracted

along QR QR is incident on the face AC and is refracted along RS PQ is the incident ray, and

RS is the emergent ray.

∠ RTK is called the angle of deviation, δ

∠ NQP = ∠ TQO = i and ∠ RQO = r1

∠ TQR = ∠ TQO – ∠ RQO = i – r1

Similarly ∠ TRQ = e – r2

δ = (i – r1) + (e – r2)

= (i – e) – (r1 + r2) (1)

Now ∠ A + ∠ QOR = 180º (2)

In ∆ QRO r1 + r2 + ∠ QOR = 180º (3)

From Eqs (2) and (3) ∠ A = r1 + r2 (4)

Let the prism be set in the position of minimum deviation, so that

δ = δm

Then r1 = r2 = r (say) and i = e

From Eq (1) δm = 2i – 2r

From Eq (2) A = 2r

2 –

m i A

or

2 sin

sin

m

A i i r

+ δ

=

=

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+sin2

sin /2

m

A A

δ

104 See Q 103.

δ = i + e – A

105 Angular dispersion for a pair of colours is the difference in the deviations suffered by those

two colours on passing through the prism If δV and δRare the deviations suffered by violet andred colours, then the angular dispersion for red and violet colours is ∆δ = δV– δR

Let µR and µVbe the refractive indices of the material of the prism for red and violet coloursrespectively Then for a small angled prism and for small angles of incidence, we have δV= (µV

– 1) A and

δR= (µR– 1) A, where A is the prism angle.

⇒ ∆δ = δV– δR= A (µV – µR)

106 Emission spectrum Spectrum of light emitted by luminous bodies is called emission

spec-trum Such spectra are of the following three types :

(i) Line spectrum A line spectrum consists of narrow bright lines separated by dark intervals.

Line spectra are emitted by substances in atomic state and are characteristic of the

sub-stances emitting them

(ii) Band Spectrum A band spectrum consists of a number of bright bands separated by dark

intervals Band spectra are emitted by substances in molecular state A band consists of a

large number of close lines

(iii) Continuous spectrum A continuous spectrum consists of an unbroken sequence of

wave-lengths (or colours) over a wide range Continuous spectra are emitted by solids, liquids andhighly compressed gases heated to high temperature A continuous spectrum is not charac-

teristic of the nature of the source but depends only on the temperature.

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107 A convex lens of short focal length is used as a simple microscope When a small object is

placed between the optical centre and the focus of a convex lens, its virtual and enlarged image

is formed The position of the object is so adjusted that the final image is formed at the least

distance of distinct vision D [See Fig 6 B 14].

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108 The compound microscope consists of two lenses of short focal lengths The lens facing the

object is called the objective and the other one, which is towards the eye, is called the eye piece.

The objective forms the image of an object placed just outside the focus This image is real,inverted and magnified It acts as an object for the eye - piece The adjustment is so done thatthe final image formed by the eyepiece is at the least distance of distinct vision

A"

B' B"

Let AB be an object placed just outside the focus Fo of objective A B′ ′is the real image formed

on the other side of the objective which lies in between the focus and the optical centre of the

eyepiece Now eyepiece acts as a simple magnifier The distance between AB and the objective

is so adjusted that a virtual and magnified image is formed at the least distance of distinctvision

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Magnifying power of a compound microscope is

109 The astronomical telescope consists of two lenses The lens facing the eye is of short focal

length and is called the eyepiece The other lens, which is near the object, is of large focallength and is called the objective

The objective forms a real and inverted image of a distant object at its focus Now the position

of the eye piece is so adjusted that the final image is formed at the least distance of distinctvision

Fig 6 B.16

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omagnifying power is given by 1

fo and feare the focal lengths of the objective and the eyepiece, respectively , and D is the

least distance of distinct vision

110. The objective forms a real, inverted and diminished image of a distant object at its focus on theother side of the objective This image A B′ ′acts as an object for the eyepiece The position ofthe eyepiece is so adjusted that A B′ ′ lies at the focus of the eyepiece (foci of objective andeyepiece coincide in this case) This image acts as an object for the eyepiece

Fig 6 B.17