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451.

A convex lens of focal length `f` is placed somewhere in between an object and a screen. The distance between the object and the screen is `x`. If the numerical value of the magnification produced by the lens is `m`, then the focal lnegth oof the lens is .A. `(mx)/((m+1)^(2))`B. `(mx)/((m-1)^(2))`C. `((m+1)^(2))/(m) x`D. `((m-1)^(2))/m x`

Answer» Correct Answer - a
452.

If the focal length of the objective lens is increased thenA. microscope will increase but that of telescope decreaseB. microscope and telescope, both will increase.C. microscope and telescope both will decreaseD. microscope will decrease, but that of telescope will increase.

Answer» Correct Answer - D
For microscope, `M = (v_0)/(-u_0) (1 + (d)/(f_e))`
and for telescope, `M = (f_0)/(f_e)(1 + (f_e)/(d))`
When we increase `f_e : M` for microscope decreases and `M` for telescope increases.
453.

Astigmation is correct by usingA. culindrical lensB. plano convex lensC. plano concave lensD. convex lens

Answer» Correct Answer - A
In this defect, eye cannot perpendicular direction clear, i.e. horizontal and vertical lines simultaneously. It is due to imperfect spherical nature of eye lens. This defect can be removed by using cylindrical lenses. (Torric lenses)
454.

If the focal length of the objective lens is increased thenA. microscope will increase but that of electroscope decreaseB. microscope and telescope both will increaseC. microscope and telescope both will decreaseD. microscope will decrease but that of telescope will increase

Answer» Correct Answer - D
For microscope, `m=(L)/(f_(v))(D)/(f_(e)) Rightarrow m alpha (1)/(f_(v))`
`"For telescope" m=(f_(v))/(f_(e)), m alpha f_(v)`
The magnifying power of microscope will decrease but the magnifying power telescopw will increase.
455.

A focal length of a lens 10cm. What is power of a lens in dipotre?A. 0.1DB. 10DC. 15DD. 1D

Answer» Correct Answer - B
Given, f=10cm and power, P=?
The power of lens, `P=(1)/("Focal length(m)")`
`P=(1)/(f(m)) RightarrowP=(100)/("f(cm)")=(100)/(10)=10D`
456.

The positions of the object `O` (real or virtual) and the image `I`(real or virtual) with respect to the optical axis of a spherical mirror is shown. Then select the possible mirror and its position to realise it. .A. concave mirror closer to objectB. concave mirror closer to imageC. convex mirror closer to objectD. convex mirror closer to image

Answer» Correct Answer - A::C
457.

A point object is kept between a plane mirror and a concave mirror facing each other. The distance between the mirrors is 22.5 cm . The distance between the mirrors is 20 cm. what should be the distance of the object from the concave mirror so that after two successive reflections the final image is formed on the object itself ? (consider first reflection from concave mirror).A. 5 cmB. 15 cmC. 10 cmD. 7.5 cm

Answer» Correct Answer - B
458.

Two plane mirrors A and B are parallel to each other and spaced 20 cm apart. An object is kept in between them at 15 cm from a. Out of the following, at which point, image is not formed in mirror a (distance measured from mirror A)A. 15 cmB. 25 cmC. 45 cmD. 55 cm

Answer» Correct Answer - C
459.

Angle of prism is `A` and its one surface is silvered. Light rays falling at an angle of incidence `2 A` on first surface return back through the same path after suffering reflection at second silvered surface. Refraction index of the material of prism isA. `2 sin A`B. `2 cos A`C. `(1)/(2) cos A`D. `tan A`

Answer» Correct Answer - b
460.

Angle of prism is `A` and its one surface is silvered. Light rays falling at an angle of incidence `2 A` on first surface return back through the same path after suffering reflection at second silvered surface. Refraction index of the material of prism isA. 2 sin AB. 2 cos AC. `(1)/(2) cos A`D. tan A

Answer» Correct Answer - B
461.

Light of wavelength `6000 Å` falls on a plane reflecting surface. The reflected wavelength is.A. `6000 Å`B. `lt 6000 Å`C. `gt 6000 Å`D. cannot say

Answer» Correct Answer - A
462.

A lamp rated at 100 cd hangs over the middle of a round table with diameter 3 m at a height of 2 m . It is replaced by a lamp of 25 cd and the distance to the table is changed so that the illumination at the centre of the table remains as before. The illumination at edge of the table becomes X times the original. Then X isA. `(1)/(3)`B. `(16)/(27)`C. `(1)/(4)`D. `(1)/(9)`

Answer» Correct Answer - a
463.

A source of light emits a continuous stream of light energy which falls on a given area. Luminous intensity is defined asA. Luminous energy emitted by the source per secondB. Luminous flux emitted by source per unit solid angleC. Luminous flux falling per unit area of a given surfaceD. Luminous flux coming per unit area of an illuminated surface

Answer» Correct Answer - b
464.

The distance between a point source of light and a screen which is 60 cm is increased to 180 cm . The intensity on the screen as compared with the original intensity will beA. `(1//9)` timesB. `(1//3)` timesC. 3 timesD. 9 times

Answer» Correct Answer - a
465.

A glass-slab is immersed in water. What will be the crirtical angle for a light ray at glass-water interface? Where `_(a)n_(g)=1.50,_(a)n_(w)=1.33 and sin^(-1)(0.887)=62.5`A. `48.8^(@)`B. `72.8^(@)`C. `62.5^(@)`D. `64.5^(@)`

Answer» Correct Answer - C
(c ) The refractive index of glass relative to water is given by,
`""_(w)n_(g)=(""_(a)n_(g))/(""_(a)n_(w))=1.50/1.33`
If C be the crirical angle at glass water interface, then
`Sin C=(1)/(""_(w)n_(g))=1.33/1.50=0.8867`
`C=sin_(.)^(-1)(0.8867)=62.5`
466.

One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 12 cm behind the silvered face. The refractive index of the glass isA. 0.4B. 0.8C. 1.2D. 1.6

Answer» Correct Answer - C
467.

One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 12 cm behind the silvered face. The refractive index of the glass isA. `0.4`B. `0.8`C. `1.2`D. `1.6`

Answer» Correct Answer - C
468.

A double convex lens is made of glass of refractive index `1.55` with both faces of same radius of curvature. Find the radius of curvature required, if focal length is `20 cm`.

Answer» Here, `mu = 1.55, R_1 = R` and `R_2 = -R, f = 20 cm`
As `(1)/(f) = (mu - 1) ((1)/(R_1) - (1)/(R_2)) :. (1)/(20) = (1.55 - 1) ((1)/( R) + (1)/(R )) = (1.10)/( R)`
`R = 20 xx 1.1 = 22 cm`.
469.

Two plane mirror are inclined at an angle of`30^(@)`.Then the first four images of an object`O`placed between the two mirrors are correctly represented byA. B. C. D.

Answer» Correct Answer - 1
The image of object`O`form mirror`M_(1)`is`I_(2)`and the imag eof`I_(1)`(the virtual object)from mirror`M_(2)`is`I_(3)`.The image of object`O` from mirror`M_(2)`is`I_(2)`and the image of`I_(2)`( the virtual object)form mirror`M_(1)`is`I_(4)`.Notice that this enterpretation ,according to ray diagram rules,si valid only for fig(1).All others are inconsistent Hence correct is (1)
470.

The refractive index of a piece of glass of `1.5`and it acomodates as many waves as are accomodated in`18cm` width of water column.If the refractive index of water `1.33`then the thickness of glass piece will be-A. `20cm`B. `10cm`C. `12cm`D. `16cm`

Answer» Correct Answer - 4
`n_(glass)=1.5`
`N_(water)=1.33`
`t_(water)=18cm`
`t_(glass)=?`
`:.n_(glass)t_(glass)=n_(water)t_(water)…….(1)`
Fromeqs.(1)and(2) …….. (2)
`t_(glass)=(1.33xx18)/(1.5)=16cm`
471.

A boy of height 1m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isA. `0.25 m`B. `0.33 m`C. `0.5 m`D. `0.67 m`

Answer» Correct Answer - C
Let f be foc al length of the convex mirror. According to new cartesiaan sign convention
Object distance, ` u = - f`, focal length `= + f`
Using mirror formula, `1/u + 1/v = 1/f`
`(1)/(-f)+1/v=1/f` or `1/v=1/f+1/f=2/f` or `v = f/2`
The image is formed at a distance `f/2` behind the mirro. It is virtual image.
Magnification, `m = -(v)/(u) = - ((f//2))/((-f)) = 1/2`
Also, `m = ("Height of image"(h_(I)))/(Height of object(h_(O)))`
`:. h_(I) = mh_(O) = 1/2 (1m) = 0.5 m`
472.

In a compound microscope, the focal length of the objective and the eye lens are `2.5 cm` and `5 cm` respectively. An object is placed at `3.75cm` before the objective and image is formed at the least distance of distinct vision, then the distance between two lenses will be `( i.e.` length of the microscope tube )A. 11.67 cmB. 12 cmC. 12.75 cmD. 13 cm

Answer» Correct Answer - A
For objective lens, `(1)/(f_(o))=(1)/(v_(o))-(1)/(u_(o))`
Using proper sign convention,
`(1)/(+2.5)=(1)/(v_(o))-(1)/((-3.75))rArr v_(o)=7.5 cm`
For eye lens, `(1)/(f_(e ))=(1)/(v_(e ))-(1)/(u_(e ))`
`(1)/(+5)=(1)/((-25))-(1)/(u_(e )) rArr u_(e )=-4.16 cm`
or `" " |u_(e )|=4.16 cm`
`therefore` Distance between the lens `= 7.5+4.16=11.67 cm`
473.

Which of the following (referred to a sphericla mirror) do (does) not depend on whether the rays are paraxial or not?A. Radius of curvatureB. FocusC. PoleD. Principle axis.

Answer» Correct Answer - A::B::C
Focus alone depends on whether the rays are paraxial or not. The rest of the three factors do not.
474.

A slab of transparent material is made as shown in Fig. Monochromatic parallel beams of light are normally incident on the slab. The thickness of `C` is twice the thickness of `B`. If the number of waves in A = number of waves in combination of `B and C`, then the refractive index of `B` is : .A. 1.33B. 1.8C. 1.6D. 1.6

Answer» Correct Answer - B
Let thickness of `B = t`
`:.` Thickness of `C = 2t`
and thickness of `A = t + 2 t = 3 t`
If `lamda_0` is wavelength in air, then as number of waves in `A = no`, waves in `B + no`. Of waves in `C`
`:. (3t)/(lamda_0//mu_0) = (t)/(lamda_0//mu_1) + (2t)/(lamda_0//mu_2)`
or `3 mu_0 = mu_1 + 2mu_2`
or `mu_1 = 3 mu_0 - 2 mu_2`
=`3 xx 1.4 - 2 xx 1.2`
=`1.8`.
475.

Two lenses of power `-15D` and `+5 D` are in contact with each other. The focal length of the combination isA. `+10cm`B. `-20cm`C. `-10cm`D. `+20cm`

Answer» Correct Answer - 1
Power of a lens is reciprocal of its local length .Power of combined lens is `
P=P_(1)+P_(2)`
`=15+5=-10D`
`:.f=(1)/(p)=(100)/(-10)cm`
or`f=-10cm`
476.

Two lenses of power 15D and -3D are placed in contact. The focal length of the combination is aA. 10cmB. 15cmC. 12cmD. 18cm

Answer» Correct Answer - D
`"Given" P_(1)=15D and P_(2)=-3D`
`therefore P=P_(1)+P_(2)=15D-3D=12D `
`therefore P=(1)/(f(m)) Rightarrow P=(100)/(f(cm)) Rightarrow 12=(100)/(f)`
Focal length of the combination, `f=(100)/(12)=8.33cm`
477.

Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length `+ 20 cm` when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is A. `+80 cm`B. `-80 cm`C. `-24 cm`D. `-100 cm`

Answer» Correct Answer - D
478.

The diameter of a plano convex lens is `6 cm` and thickness at the centre is `3 mm`. If the speed of light in the material of the lens is `2 xx 10^8 m//s`, what is the focal length of the lens ?A. 15 cmB. 20 cmC. 30 cmD. 10 cm

Answer» Correct Answer - C
Here, `d = 6 cm, h = 3 mm= 0.3 cm`,
`v = 2 xx 10^8 m//s, f = ?`
If `R` is radius of curvature of the convex surface of lens, then from
`((d)/(2))^2 = (2 R - h) h = 2 R h` `(because h lt lt R)`
`R = (d^2//4)/(2 h) = (6^2//4)/(2 xx 0.3) = 15 cm`
`mu = ( c)/(v) = (3 xx 10^8)/(2 xx 10^8) = (3)/(2)`
From `(1)/(f) = (mu -1) ((1)/(R_1) - (1)/(R_2))`
=`((3)/(2) - 1) ((1)/(oo) + (1)/(15)) = (1)/(30)`
`f = 30 cm`.
479.

When white light enters a prism, it gets split into its constituent colours. This is due toA. High density of prism materialB. Because `mu` is different for different `lambda`C. Diffraction of lightD. Velocity changes for different frequencies

Answer» Correct Answer - b
480.

Which of the prism is used to see infra-red spectrum of lightA. Rock SaltB. NicolC. FlintD. Crown

Answer» Correct Answer - a
481.

Focussing in a compound microscope is carried out by changing the……..from the……… .

Answer» distance of objective lens , object.
482.

In an astronomical telescope, the distance between……….and…….can be varied.

Answer» objective lens , eye lens.
483.

In normal adjusment of telescope, final image is……. . And distance between objective lens and eye lens is………. .

Answer» at infinity , `(f_0 + f_e)`.
484.

A concave mirror cannot fromA. virtual image of virtual objectB. virtual image of a real objectC. real image of a real objectD. real image of a virtual object

Answer» Correct Answer - A
485.

A thin lens of focal length `f` is used as magnifying glass..Which of the following statement regardind the situations is true?A. A converging lens may be used,and the object be placed at a distance between greater than`2f`B. A diverging lens may be used ,and the object be placed between `f`and`2f`C. A converging lens may be used,and the object be placed at a distance less than`f` from lens.D. A diverging lens may be used.,and the object be at any point other than focal point

Answer» Correct Answer - C
486.

Why do we prefer a magnifying glass of smaller focal length ?

Answer» This is because the magnifying power is more when focal length is short.
487.

State the factors on which refractive index of a medium depend ?

Answer» Refractive index of a medium depends on
(i) nature of medium
(ii) wavelength of light used
(iii) temeprature
(iv) nature of surrounding medium.
488.

A ray of light is incident on a surface of glass slab at an angle `45^@`. If the lateral shift produced per unit thickness is `1//sqrt3`, the angle of refraction produced isA. `tan^(-1)(sqrt3/2)`B. `tan^(-1)(1-sqrt(2/3))`C. `sin^(-1)(1-sqrt(2/3))`D. `tan^(-1)(sqrt(2/(sqrt3-1)))`

Answer» Correct Answer - B
(b) Here, angle of incidencei=`45^(@)`
`("Lateral shift(d)")/("Thickness of glass slab(t)")=1/sqrt3`
Lateral shift,d=`(tsindelta)/(cosr)=(tsin(i-r))/(cosr)`
`rArr d/t=(sin(i-r))/(cosr)`
or `d/t=(sinicosr-cosisinr)/(cosr)`
`=(cosr-sinr)/(sqrt2cosr)`
or `d/t=1/sqrt2(1-tanr)or1/sqrt3=1/sqrt2(1-tanr)`
or `tanr=1-(sqrt2)/(sqrt3)`
or Angle of refraction, r=`tan^(-1)(1-(sqrt2)/(sqrt3))`
489.

The true statement isA. he order of colours in the primary and the secondary rainbows is the sameB. The intensity of colours in the primary and the secondary rainbows is the sameC. The intensity of light in the primary rainbow is greater and the order of colours is the same than the secondary rainbowD. The intensity of light for different colours in primary rainbow is greater and the order of colours is reverse than the secondary rainbow

Answer» Correct Answer - d
490.

What will be the colour of sky as seen from the earth, if there were no atmosphereA. BlackB. BlueC. WhiteD. Red

Answer» Correct Answer - A
(a) Sky appears blue due to scattering. In absence of atmosphere no scattering will occur. Therefore sky will be seen black.
491.

What will be the colour of sky as seen from the earth, if there were no atmosphereA. BlackB. BlueC. OrangeD. Red

Answer» Correct Answer - a
492.

Colour of the sky is blue due toA. Scattering of lightB. Total internal reflectionC. Total emissionD. None of the above

Answer» Correct Answer - a
493.

Which of the following spectrum have all the frequencies from high to low frequency rangeA. Band spectrumB. Continuous spectrumC. Line spectrumD. Discontinuous spectrum

Answer» Correct Answer - b
494.

Stars are not visible in the day time becauseA. Stars hide behind the sunB. Stars do not reflect sun rays during dayC. Stars vanish during the dayD. Atmosphere scatters sunlight into a blanket of extreme brightness through which faint stars cannot be visible

Answer» Correct Answer - d
495.

Which of the following colours suffers maximum deviation in a prismA. YellowB. BlueC. GreenD. Orange

Answer» Correct Answer - b
496.

Light from sodium lamp is passed through cold sodium vapours the spectrum of transmitted light consists ofA. A line at 5890 ÅB. A line at 5896 ÅC. Sodium doublet linesD. No spectral features

Answer» Correct Answer - d
497.

Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism The angle of prism is `(cos 41^(@) = 0.75)`A. `62^(@)`B. `41^(@)`C. `82^(@)`D. `31^(@)`

Answer» Correct Answer - c
498.

When light of wavelength `lambda` on an equilateral prism, kept on its minimum deviation position, it is found that the angle of deviation equals the angle the angle of the prism itself. The refractive index of the material of the prism for the wavelength `lambda` isA. `sqrt3`B. `(sqrt3)/2`C. 2D. `sqrt2`

Answer» Correct Answer - A
(a) Refractive index for prism,
`µ=(sin""((A+delta_(m))/2))/(sin""(A/2))=(sin((60^(@)+60^(@))/2))/(sin""((60^(@))/2))=sqrt3`
499.

In a thin prism of glass (refractive index 1.5), which of the following relations between the angle of minimum deviations `delta_(m)` and angle of prism r will be correct?A. `delta_(m)=r`B. `delta_(m)=1.5r`C. `delta_(m)=2r`D. `delta_(m)=r/2`

Answer» Correct Answer - A
(a) Angle of minimum deviation in prism,
`delta_(m)=(µ-1)A=(µ-1)(2r) (thereforer=A//2)`
`=(1.5-1)(2r)=0.5xx2r=r`
500.

Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism The angle of prism is `(cos 41^(@) = 0.75)`A. `21^(@)`B. `42^(@)`C. `60^(@)`D. `82^(@)`

Answer» Correct Answer - D
(d) Refractive index of prism, µ`=(sin""((A+delta_(m))/2))/(sin(A/2))`
substituting `A=delta_(m)and µ=1.5,`
`1.5=(sinA)/(sin((A/2)))`
`(1.5)/2=cos""A/2`
`7.5=cos""A/2`
We get, A=`82^(@)`.