Chapter # 20
Dispersion and Spectra
SOLVED EXAMPLES
1.
Find the dispersive power of flint glass. The refractive indices of flint glass for red, yellow and violet light are 1.613, 1.620 and 1.632 respectively.
Sol.
The dispersive power is = =
µv µr µ 1
1.632 1.613 = 0.0306. 1.620
2.
The focal length of a thin lens for red and violet light are 90.0 cm and 86.0 cm respectively. Find the dispersive power of the material of the lens. Make appropriate assumptions.
Sol.
We have
1 = (µ – 1) f
1 1 R R 2 1
K 1 1 , = . f 1 1 f R1 R 2
or,
µ –1=
Thus,
K µv – 1 = f v
and,
1 1 so that µv – µr = K f f r v Also, we can assume that µy – 1 =
=
K µr – 1 = f r 1 1 = K 86 .4 cm 90cm = K × 4.6 × 10–1.
µv µr µv 1 µr 1 –1= + 2 2 2
1 1 K –2 –1 86 . 4 cm 90 cm = K × 1.1 × 10 cm . 2
Thus, the dispersive power of the material of the lens is
µv µr 4.6 10 4 = µ 1 = = 0.042. y 1.1 10 2
QUESTIONS 1.
The equation w =
FOR
SHORT
ANSWER
µv µr was derived for a prism having small refracting angle. It is also valid for a prism of µ 1
large refracting angle? it is also valid for a glass slab or a glass sphere ?
2.
Can the dispersive power =
µv µr be negative? What is the sign of if a hollow prism is immersed into µ 1
water? 3.
If three identical prisms are combined, it is possible to pass a beam the emerges undeviated? Undispersed?
4.
“Monochromatic light should be used to produced pure spectrum”. Comment on this statement.
5.
Does focal length of a lens depend on the colour of the light used? Does focal length of a mirror depend on the colour?
6.
Suggest a method to produce a rainbow in your house. manishkumarphysics.in
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Chapter # 20
Dispersion and Spectra
Objective - I 1.
The angular dispersion produced by a prism (A*) increases if the average refractive index increases (B) increases if the average refractive index decreases (C) remains constant whether the average refractive index increases or decreases (D) has no relation with average refractive index fizTe }kjk izkIr dks.kh; o.kZ fo{ksi.k (A*) c<+rk gS] ;fn vkSlr viorZukad c<+rk gSA (B) c<+rk gS] ;fn vkSlr viorZukad ?kVrk gSA (C) vpj jgrk gS] pkgs vkSlr viorZukad ?kVs ;k c<+As (D) vkSlr viorZukad ds lkFk dksbZ lac/a k ugha gSA
2.
If a glass prism is dipped in water, its dispersion power (A) increases (B*) decreases (C) does not change (D) may increase or decreases depending on whether the angle of the prism is less than or greater than 60° ;fn dk¡p ds fizTe dks ikuh esa Mqcks;k tk;s rks bldh o.kZ fo{ksi.k {kerk (A) c<+rh gSA (B*) ?kVrh gSA (C) ifjofrZr ugha gksrh gSA (D) c<+ Hkh ldrh gS ;k ?kV Hkh ldrh gSA ;g bl ij fuHkZj gS fd fizTe dks.k 60° ls de gS ;k vf/kd gSA
3.
A prism can produced a minimum deviation in a light beam. If three such prism are combined, the minimum deviation that can be produced in this beam is ,d fizTe] izdk'k iqat esa U;wure fopyu mRiUu dj ldrk gSA ;fn bl izdkj ds rhu fizTe la;ksftr fd;s tk;s rks bl iqat esa mRiUu fd;k tk ldus okyk U;wure fopyu gksxk (A) 0 (B*) (C) 2 (D) 3
4.
Consider the following two statements : (i) line spectra contain information about atoms (ii) bond spectra contain information about molecules (A) both i and ii are wrong (B) i is correct but ii is wrong (C) ii is correct but i is wrong (D*) both i and ii are correct fuEufyf[kr nks dFkuksa ij fopkj dhft;s (i) js[kh; LisDVªe ls ijek.kqvksa ds ckjs esa tkudkjh izkIr gksrh gSA (ii) cS.M LisDVªe ls v.kqvksa ds ckjs esa tkudkjh izkIr gksrh gSA (A) (i) o (ii) nksuksa vlR; gSA (B) (i) lR; gS] ijUrq ii vlR; (C) (ii) lR; gS] ijUrq (i) vlR; gSA (D*) (i) o (ii) nksuksa lR; gSA
5.
gSA
The focal length of a converging lens are fv and fr for violet and red light respectively. (A) fv > fr (B) fv – fr (C*) fv < fr (D) any of the three is possible depending on the value of the average refractive index µ cSxa uh o yky izdk'k ds fy, mÙky ySl a dh Qksdl nwjh Øe'k% fv o fr gS rks (A) fv > fr (B) fv – fr (C*) fv < fr (D) mijksDr rhuksa esl a s dksbZ Hkh laHko gSA ;g vkSlr viorZukad µ ds eku ij fuHkZj djrk gSA
Objective - II 1.
A narrow beam of white light goes through a slab having parallel faces. (A) the light never splits in different colours (B*) the emergent beam is white (C*) the light inside the slab is split into different colours (D) the light inside the slab is white
tc ,d ladh.kZ 'osr izdk'k iqat ,slh ifV~Vdk ¼Lysc½ ls xqtjrk gS] ftlds Qyd lekUrj gS] rks (A) izdk'k dHkh Hkh fofHkUu jaxksa esa foHkkftr ugha gksrk gSA manishkumarphysics.in
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Chapter # 20
Dispersion and Spectra
(B*) fuxZfer iqat] 'osr gksrk gSA (C*) ifV~Vdk ds vUnj izdk'k fofHkUu jaxksa esa (D) ifV~Vdk ds vUnj izdk'k 'osr gksrk gSA
foHkkftr gks tkrk gSA
2.
By properly combining two prisms made of different materials, it is possible to (A*) have dispersion without average dispersion (B*) have deviation without dispersion (C*) have both dispersion and average deviation (D) have neither dispersion nor average deviation fofHkUu inkFkks± ls cus nks fizTeksa dks Bhd rjg ls la;D q r djds ;g laHko gS (A*) vkSlr fopyu jfgr o.kZ fo{ksi.k (B*) o.kZ fo{ksi.k jfgr fopyu (C*) o.kZ fo{ksi.k o vkSlr fopyu nksuksa (D) uk rks o.kZ fo{ksi.k o u gh vkSlr fopyu
3.
In producing a pure spectrum, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens because a narrow slit (A) produces less diffraction (B) increases intensity (C) allows only one colour at a time (D*) allows a more parallel beam when it passes through the lens
'kq) LisDVªe izkIr djus ds fy, vkifrr izdk'k dks vo.kZd ySl a dh Qksdl nwjh ij j[ks ,d js[kkfNnz ls xqtkjrs gS]a D;ksfa d js[kkfNnz (A) cgqr de foorZu mRiUu djrk gSA (B) rhozrk c<+krk gSA (C) ,d le; esa ,d jax dks tkus nsrk gSA (D*) tc ;g ySl a ls xqtjrk gS rks vf/kd lekUrj iqt a dks tkus nsrk gSA 4.
Which of the following quantities related to a lens depend on the wavelength of wavelengths of the incident light? (A*) power (B*) focal length (C*) chromatic aberration (D) radii of curvature ySl a ls lacaf/kr dkSulh jkf'k vkifrr izdk'k dh rjaxnS/;Z ij fuHkZj djrh gS (A*) 'kfDr (B*) Qksdl nwjh (C*) o.kZ foiFku (D) oØrk f=kT;k
5.
Which of the following quantities increase when wavelength is increased? Consider only the magnitudes. (A) the power of a converging lens (B*) the focal length (C) the power of a diverging lens (D*) the focal length of a diverging lens. tc rjaxnS/;Z esa o`f) djrs gSa rks dsoy ifjek.k dh n`f"V ls dkSulh jkf'k esa o`f) gksrh gS (A) mÙky ySal dh {kerk esaA (B*) mÙky ySal dh Qksdl nwjh esaA (C) vory ySl a dh {kerk esAa (D*) vory ySal dh Qksdl nwjh esAa
WORKED OUT EXAMPLES 1.
The refractive indices of flint glass for red and violet light are 1.613 and 1.632 respectively. Find the angular dispersion produced by a thin prism of flint glass having refracting angle 5°.
Sol.
Deviation of the red light is r = (µr – 1) A and deviation of the violet light is v = (µv – 1)A. The dispersion = v – r = (µv – µr)A = (1.632 – 1.613) × 5° = 0.095°.
2.
A crown glass prism of angle 5° is to be combined with a flint glass prism in such a way that the mean ray passes undeviated. Find (a) the angle of the flint glass prism needed and (b) the angular dispersion produced by the combination when white light goes through it. Refractive indices for red, yellow and violet light are 1.514, 1.517 and 1.523 respectively for crown glass and 1.613, 1.620 and 1.632 for flint glass. manishkumarphysics.in
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Chapter # 20 Sol.
(a)
The deviation produced by the crown prism is = (µ – 1) A and by the flint prism is = (µ – 1) A The prisms are placed with their angles inverted with respect to each other. The deviation are also in opposite directions. Thus, the net deviation is D = – = (µ – 1)A – (µ – 1)A If the net deviation for the mean ray is zero, (µ – 1)A = (µ –– 1)A.
(µ 1) 1.517 1 A= × 5° (µ 1) 1.620 1 The angular dispersion produced by the crown prism is v – r = (µv – µr) A and that by the flint prism is v – r = (µv – µr) A The net angular dispersion is, = (µv – µr)A – (µv – µr)A = (1.523 – 1.514) × 5° – (1.632 – 1.613) × 4.2° = – 0.0348°. The angular dispersion has magnitude 0.0348. or,
(b)
Dispersion and Spectra
A=
3.
The dispersive powers of crown and flint glasses are 0.03 and 0.05 respectively. The refractive indices for yellow light for these glasses are 1.517 and 1.621 respectively. It is desired to form an achromatic combination of prism of crown and flint glasses which can produce a deviation of 1° in the yellow ray. Find the refracting angles of the two prism needed.
Sol.
Suppose, the angle of the crown prism needed is A and that of the flint prism is A. We have =
µv µr µ 1
or, µv – µr = (µ – 1). The angular dispersion produced by the crown prism is (µv – µr) A = (µ – 1)A. Similarly, the angular dispersion produced by the flint prism is (µ – 1)A. For achromatic combination, the net dispersion should be zero. Thus, (µ – 1) A = (µ – 1) wA
(µ 1) 0.517 0.03 A = = = 0.50. .............(i) (µ 1) 0.621 0.05 A The deviation in the yellow ray produced by the crown prism is = (µ – 1)A and by the flint prism is = (µ – 1)A. The net deviation produced by the combination is – = (µ – 1) A – (µ – 1) A or, 1° = 0.517 A – 0.621 A .............(ii) solving (i) and (ii), A = 4.8° and A = 2.4°. Thus, the crown prism should have its refracting angle 4.8° and that of the flint prism should be 2.4°. or,
EXERCISE 1.
A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of crown prism?
,d f¶yaV dkap o Økmu dk¡p ds fizTe dks bl izdkj la;D q r fd;k tkrk gS fd ek/; fdj.k dk fopyu 'kwU; gkskrk gSA f¶yaV rFkk Økmud dk¡p dk ek/; fdj.k ds fy, viorZukad Øe'k% 1.620 o 1.518 gSA ;fn f¶yaV fizTe dk viorZu dks.k 6.0°gS] rks Økmu fizTe ds fy, viorZu dks.k D;k gksxk\ Ans. 7.2°
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Chapter # 20 Dispersion and Spectra 2. A certain material has refractive indices 1.56, 1.60 and 1.68 for red, yellow and violet light respectively. (a) Calculate the dispersive power. (b) Find the angular dispersion produced by a thin prism of angle 6° made of this material. ,d inkFkZ dk yky] ihys o cSxa uh izdk'k ds fy, viorZukad Øe'k% 1.56, 1.60 o 1.68 gS :- (a) o.kZ fo{ksi.k {kerk Kkr dhft;sA (b) bl inkFkZ ls cus 6° dks.k ds irys fizTe }kjk mRiUu dks.kh; o.kZ fo{ksi.k Kkr dhft;sA Ans. (a) 0.2° (b) 0.72° 3.
The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens. ,d mÙky ySal dh yky] ihys ,oa cSaxuh fdj.kksa ds fy, Qksdl nwjh Øe'k% 100 lseh] 98 lseh ,oa 96 lseh gSA bl inkFkZ
ds ySl a o.kZ fo{ksi.k {kerk Kkr dhft;sA Ans. 0.041 4.
The refractive index of a material changes by 0.014 as the colour of the light changes from red to violet. A rectangular slab of height 2.00 cm made of this material is placed on a newspaper. when viewed normally in yellow light, the letters appear 1.32 cm below the top surface of the slab. Calculate the dispersive power of the material. izdk'k dk jax yky ls cSxa uh gksus ij inkFkZ dk viorZukad esa Hkh 0.014 dk ifjofrZr gks tkrk gSA bl inkFkZ ls cuh 2.00
lseh Å¡pkbZ dh vk;rkdkj ifV~Vdk dks v[kckj ij j[kk tkrk gSA tc ihys izdk'k esa vfHkyEcor~ ns[kk tkrk gSA rks 'kCn ifV~Vdk ds Åijh fljs ls 1.32 lseh uhps fn[kkbZ nsrs gSaA inkFkZ dh o.kZ fo{ksi.k {kerk Kkr dhft;sA Ans. 0.026 5.
A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing though the prism suffers a minimum deviation of 4.0° in favourable conditions. Calculate the angle of the prism. ,d iryk fizTe ml inkFkks± ls cuk gS] ftldk yky o cSxa uh izdk'k ds fy, viorZukad 1.61 o 1.65 gSA inkFkZ dh o.kZ fo{ksi.k {kerk 0.07 gSA ;g ik;k tkrk gS fd mfpr ifjfLFkfr;ksa ihys izdk'k ds iqt a dk fizTe ls xqtjus ij U;wure fopyu 4.0°
gS] fizTe dks.k Kkr dhft;sA Ans. 7° 6.
The minimum deviation suffered by red, yellow and violet beams passing through an equilateral transparent prism are 38.4°, 38.7° and 39.2° respectively. Calculate the dispersive power of the medium. ,d leckgq ikjn'khZ fizTe ls xqtjus okys yky] ihys o uhy iqat ds fy;s U;wure fopyu Øe'k% 38.4°, 38.7° o 39.2°
gSA ek/;e dh o.kZ fo{ksi.k {kerk Kkr dhft;sA Ans. 0.0206 7.
Two prisms of identical geometrical shape are combined with their refracting angles oppositely shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by 1.0° when passes symmetrically through this combination. What is the angle of the prism?
leku T;kferh; vkÑfr ds nks fizTeksa dks bl izdkj la;D q r fd;k fd muds viorZu dks.k foijhr fn'kk esa gSA fizTeksa ds inkFkks± dk cSxa uh izdk'k ds fy, viorZukad 1.52 o 1.62 gSA tc cSxa uh fdj.k bl la;kstu ls lefer xqtjrh gS rks 1.0° fopfyr gks tkrh gSA fizTeksa dks dks.k fdruk gS\ Ans. 10° 8.
Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are µr, µy and µv respectively and those for the flint glass are µr, µy and µu respectively. Find the ratio A/A for which (a) there is no net angular dispersion, and (b) there is no net deviation in the yellow ray.
fp=kkuqlkj rhu irys fizTeksa dks la;qDr fd;k tkrk gSA yky] ihyh rFkk cSxa uh fdj.kksa ds fy, ØkWmu dk¡p ds fy, Øe'k% µr, µy rFkk µv ,oa f¶yaV dk¡p ds fy, Øe'k% µr, µy rFkk µu gSA A/A dk vuqikr Kkr dhft;sA ftlds fy, (a) dksbZ dqy dks.kh; fo{ksi.k ugha gS rFkk (b) ihyh fdj.k esa dksbZ dqy fopyu ugha gSA
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Chapter # 20 2(µ y 1) Ans. (a) µ 1 y
9.
Dispersion and Spectra
2(µv µr ) (b) µ µ v r
A thin prism of crown glass (µr = 1.515, µv = 1.525) and a thin prism of flint glass (µr = 1.612, µv = 1.632) are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate the angular dispersion produced by the combination. ØkWmu dk¡p (µr = 1.515, µv = 1.525) o f¶yaV dk¡p (µr = 1.612, µv = 1.632) ds irys fizTeksa dks ,d nwljs ds lEidZ esa j[kk tkrk gSA mudk izR;sd dk viorZu dks.k 5.0° gS rFkk ;s ,d leku fn'kk esa gSA bl la;kstu ls izkIr dks.kh; fo{ksi.k
Kkr dhft;sA Ans. 0.15° 10.
A thin prism of angle 6.0°, = 0.07 and µy = 1.50 is combined with another thin prism having = 0.08 and µy = 1.60. The combination produces no deviation in the mean ray. (a) Find the angle of the second prism. (b) Find the net angular dispersion produced by the combination when a beam of white light passes through it. (c) If the prisms are similarly directed, what will be the deviation in the mean ray? (d) Find the angular dispersion in the situation described in (c). = 0.07 , µy = 1.50 o 6.0° dks.k okys irys fizTe dks ,d nwljs fizTe = 0.08 o µy = 1.60 ds lkFk la;D q r fd;k tkrk gSA bl la;kstu ls ek/; fdj.k esa dksbZ fopyu ugha gksrk gSA (a) nwljs fizTe dk dks.k Kkr dhft;sA (b) tc 'osr izdk'k iqat blls xqtjrk gS rks bl la;kstu }kjk izkIr dqy dks.kh; fo{ksi.k Kkr dhft;sA (c) ;fn fizTe leku fn'kk esa gS rks ek/ ; fdj.k esa fdruk fopyu gksxkA (d) Hkkx (c) esa O;Dr fLFkfr ds fy;s dks.kh; fo{ksi.k Kkr dhft;sA Ans. (a) 5° (b) 0.03° (c) 6° (d) 0.45°
11.
The refractive index of a material M1 changes by 0.014 and that of another material M2 changes by 0.024 as the colour of the light is changed from red to violet. Two thin prisms one made of M1(A = 5.3°) and other made of M2(A = 3.7°) are combined with their refracting angles oppositely directed. (a) Find the angular dispersion produced by the combination. (b) The prism are now combined with their refracting angles similarly directed. Find the angular dispersion produced by the combination. tc izdk'k dk jax yky ls cSxa uh fd;k tkrk gS rks inkFkZ M1 dk viorZukad 0.014 rFkk nwljs inkFkZ M2 dk viorZukad 0.024 ifjofrZr gks tkrk gSA nks irys fizTeksa dks la;D q r fd;k tkrk gS] ftuesa ls ,d M1(A = 5.3°) rFkk nwljk M2(A = 3.7°) dk cuk gqvk gS] rFkk muds viorZu dks.k dh fn'kk foijhr gSA (a) bl la;kstu ls izkIr dks.kh; fo{ksi.k Kkr dhft;sA (b) vc
fizTeksa dks bl izdkj la;qDr fd;k tkrk gS fd mudh fn'kk leku gS] bl la;kstu }kjk izkIr dks.kh; fo{ksi.k Kkr dhft;sA Ans. (a) 0.0146°
(b) 0.163°
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