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801.

An eye specialist prescribes spectacles having combination of convex lens of focal length 40cm in contact with a concave lens of focal length 25cm. The power of this lens combination in diopters isA. `+1.5 D`B. `-1.5D`C. `+6.67`DD. `-6.67D`

Answer» Correct Answer - B
(b) `therefore` power of the lens=`1/"Focal length"`
focal length of combination of convex and cocave lenses is given by
`1/F=1/(f_(1))=1/F_(2)`
Where, `f_(1)` and `f_(2)` be the focal lengths of convex and concave lenses, respectively
Now, `1/F=1/0.4=1/((-0.25))`
`1/F=-1.5`
Power, P=-1.5D
802.

An eye specialist prescribes spectacles having combination of convex lens of focal length 40cm in contact with a concave lens of focal length 25cm. The power of this lens combination in diopters isA. `+ 1.5`B. `- 1.5`C. `+ 6.67`D. `- 6.67`

Answer» Correct Answer - b
803.

An eye specialist prescribes spectacles having combination of convex lens of focal length 40cm in contact with a concave lens of focal length 25cm. The power of this lens combination in diopters isA. `+1.5 D`B. `-1.5 D`C. `+6.67 D`D. `-6.67 D`

Answer» Correct Answer - B
Power of the lens combination is
`P=P_(1)+P_(2)=(1)/(f_(1)("in m"))+(1)/(f_(2)("in m"))=(1)/(+0.40"m")+(1)/(-0.25"m")`
` " "=-1.5 "m"^(-1)= -1.5 D.`
804.

Find the refractive index of the material, if a prims having an angle `A=60^(@)` which produces a minimum deviation of `30^(@)`.A. `sqrt(3)`B. `sqrt(2)`C. `sqrt(5)`D. `1/(sqrt(2))`

Answer» Correct Answer - (b)
805.

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach on the face BC if. A. `sin theta ge 8/9`B. `sin theta ge 2/3`C. `sin theta =(sqrt(3))/2`D. `2/3 lt sin theta lt 8/9`

Answer» Correct Answer - (a)
806.

A concavo-convex lens is made of glass of refractive index `1.5.` The radii of curvature of its two surfaces are `30 cm` and `50 cm.` Its focal length when placed in a liquid of refractive index `1.4` isA. `-407 cm`B. `250 cm`C. `125 cm`D. `25 cm`

Answer» Correct Answer - a
807.

A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as aA. Convergent lens of focal length 3.5 RB. Convergent lens of focal length 3.0 RC. Divergent lens of focal length 3.5 RD. Divergent lens of focal length 3.0 R

Answer» Correct Answer - a
808.

The graph in shows the variation of image distance (v) with object distance (u) in case of a lens. Find focal length of the lens. What is the nature of the lens, if image formed is real ? .

Answer» As the image formed is real, the lens must be convex.
From the graph,
when `|u| = 20 cm, |v| = 20 cm`
`:. u = -20 cm, v = + 20 cm`
`(1)/(f) =(1)/(v)-(1)/(u)=(1)/(20)+(1)/(20) = (1)/(10)`
`f = 10 cm`.
809.

A student measures the focal length of a convex lens by putting an object pin at a distance `u` from the lens and measuring the distance `v` of the image pin. The graph between `u` and `v` plotted by the student should look likeA. B. C. D.

Answer» Correct Answer - 2
For real image u is (-)and
v is (+)and`(1)/(v)-(1)/(u)=(1)/(f)`constant
810.

The lens formula isA. `(1)/(f) = (1)/(v)+(1)/(u)`B. `(1)/(f)=(1)/(v)-(1)/(u)`C. `(1)/(f)-(1)/(v) = (1)/(u)`D. `(1)/(f)-(1)/(u)=(1)/(v)`.

Answer» Correct Answer - B
The lens is formula is `(1)/(f)=(1)/(v)-(1)/(u)`.
811.

The shape of graph between `1//u` and `1//v` in case of a convex lens is Fig.A. .B. .C. .D. .

Answer» Correct Answer - A
In case of a convex lens, `u` is negative, `v` is positive.
Also `(1)/(v)-(1)/(u)=(1)/(f) =` constant 1. Therefore, shape of graph between `1//4` and `1//v` is as shown in Fig.
812.

A convex refracting surface of radius of curvature `20 cm` separates two media of refractive indices `4//3 and 1.60`. An object is placed in the first medium `(mu = 4//3)` at a distance of `200 cm` from the refracting surface. Calculate the position of image formed.A. `120 cm`B. `240 cm`C. `100 cm`D. `60 cm`

Answer» Correct Answer - B
Using, `- (mu_(1))/(mu) + (mu_(2))/(v) = (mu_(2) - mu_(1))/(R)`
Here, `R = 20 cm, mu_(1) = 4/3 . Mu_(2) = 1.60, u = - 200 cm`
`:. - (4//3)/(-200) + (1.60)/(v) = (1.60 - (4//3))/(20) rArr v = 240 m`
813.

A prism can have a maximum refracting angle of `(theta_C=`critical angle for the material of prism )A. `60^(@)`B. CC. 2CD. slightly less than than `180^(@)`

Answer» Correct Answer - C
(c ) For `Agt2C`, the ray of light does not emerge from the opposie fall of the prism.
814.

A slab of a material of refractive index 2 shown in fig. has a curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right CD is water with refractive indices as given in the figure. An object O is placed at a distance of 15 cm from the pole P as shown. The distance of the final image of O from P, as viewed from the left is......A. 20 cmB. 30 cmC. 40 cmD. 50 cm

Answer» Correct Answer - b
815.

A monochromatic beam of light passes from a denser medium into a rarer medium. As a resultA. Its velocity increasesB. Its velocity decreasesC. Its frequency decreasesD. Its wavelength decreases

Answer» Correct Answer - a
816.

The light reflected by a plane mirrorr may form a real imageA. If the rays incident on the mirror are divergingB. If the rays incident on the mirror are convergingC. If the object is placed very close to the mirrorD. Under no circumstances

Answer» Correct Answer - b
817.

Assertion `:` The size of the mirrorr affect the nature of the image. Reason `:` Small mirrorrs always forms a virtual image.A. If both assertion and reason are true and the reason is the correct explanation of the assertionB. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is falseD. If the assertion and reason both are false

Answer» Correct Answer - d
818.

For a concave mirrorr, if virtual image is formed, the graph between `m` and `u` is of the formA. B. C. D.

Answer» Correct Answer - b
819.

A man runs towards a mirrorr at a speed `15m//s.` The speed of the image relative to the man isA. `15 ms^(-1)`B. `30 ms^(-1)`C. `35 ms^(-1)`D. `20 ms^(-1)`

Answer» Correct Answer - b
820.

A man runs towards a mirrorr at a speed `15m//s.` The speed of the image relative to the man isA. 7.5 m/sB. 15 m/sC. 30 m/sD. 45 m/s

Answer» Correct Answer - b
821.

The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit `S` and the collimating lengs `L` is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure. A. 1B. 3C. 2D. None of the figures

Answer» Correct Answer - c
822.

The speed of light in media `M_1` and `M_2` are `1.5 xx 10^8 m//s and 2.0 xx 10^8 m//s` respectively. A ray of light enters from medium `M_1` to `M_2` at an incidence angle `i`. If the ray suffers total internal reflection, the value of `i` is.A. Equal to `sin^-1((2)/(3))`B. Equal to or less than `sin^-1((3)/(5))`C. Equal to or grater than `sin^-1((3)/(4))`D. Less than `sin^-1((2)/(3))`

Answer» Correct Answer - C
Given, `v_1 = 1.5 xx 10^8 m//s , v_2 = 2.0 xx 10^8 m//s`
Refractive index for medium `M_1` is
`mu = ( c)/(v_1) = (3 xx 10^8)/(1.5 xx 10^8) = 2`
Refractive index for medium `M_2` is
`mu_2 = ( c)/(v_2)=(3 xx 10^8)/(2.0 xx 10^8) = (3)/(2)`
If `i` is the angle of incidence and `C` is the critical angle then for total internal reflection.
`sin i ge sin C`
But `sin C = mu_2//mu_1`
`:. sin i ge (mu_2)/(mu_1) ge (3//2)/(2)` or `i ge sin^-1((3)/(4))`.
823.

Find the distance of an object from a convex lens if image is two times magnified. Focal length of the lens is `10cm`

Answer» Convex lens forms both type of images real as well as virtual. Since, nature of the image is not mentioned in the question, we will have to consider both the cases.
When image is real Means v is positive and u is negative with `absv=2absu`. Thus if
u=-x then, v=2x and f=10 cm
Substituting in ,`1/v-1/u=1/f`
we have, `1/(2x)+1/x=1/10or3/(2x)=1/10`
`therefore x=15 cm`
x=15 cm , means object lies between F and 2F.
When image is virtual Means v and u both are negative. So let
u=-y then v=-2y and f=10 cm
Substituting in,`1/v-1/u=1/f`
we have, `1/(-2y)+1/y=1/10or1/(2y)=1/10`
`therefore` y=5 cm
y=5 cm, means object lies between F and P.
824.

Two thin converging lenses are placed on a common axis, so that the centre of one of them coincides with the focus of the other. An object is placed at a distance twice the focal length from the left hand lens. Where will its image be? What is the lateral magnification? The focal of each lens is f.

Answer» Here,`f_(1)=+5.0 cm and f_(2)=-10.0 cm`
Therefore, the combined focal length F is given by
`1/F=1/(f_(1))+1/(f_(2))=1/5.0-1/10.0=+1/10.0`
`therefore` F=+b10.0 cm
i.e., the combination behaves as a converging lens of focal length 10.0 cm.
825.

A lens haivng focal length and aperture of diameter d forms an image of intensity `I`. Aperture of diameter `d/2` in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively.A. `f and (I)/(4)`B. `(3 f)/(4) and (I)/(2)`C. `f and (3 I)/(4)`D. `(f)/(2) and (I)/(2)`

Answer» Correct Answer - C
By convering the aperture of diameter `d//2`, focal length of lens is not affected. Area reduces by `1//4 th`. So does the intensity.
New focal length `= f` and
New intensity `= I - (I)/(4) = (3 I)/(4)`.
826.

n a parallel beam of white light is incident on a converging lens, the colour which is brought to focus nearest to the lens isA. VioletB. RedC. The mean colourD. All the colours together

Answer» Correct Answer - a
827.

An achromatic combination of lenses producesA. Coloured imagesB. Highly enlarged imageC. Images in black and whiteD. Images unaffected by variation of refractive index with wavelength

Answer» Correct Answer - d
828.

If aperture of lens is halved then image will beA. No effect on sizeB. Intensity of image decreaseC. Both (a) and (b)D. None of these

Answer» Correct Answer - c
829.

Two plane mirrors are placed parallel to each other at a distance L apart. A point object O placed between them, at a distance `L//3` from obe mirror. Both mirros form multiple image. The distance between any two images cannot beA. `(3L)/(2)`B. `(2L)/(3)`C. `2L`D. `L`

Answer» Correct Answer - A
830.

When the convergent nature of a convex lens will be less as compared with airA. In waterB. In oilC. In both (a) and (b)D. None of these

Answer» Correct Answer - c
831.

The distance v of the real image formed by a convex lens is measured for various object distance u . A graph is plotted between v and u , which one of the following graphs is correctA. B. C. D.

Answer» Correct Answer - d
832.

Can a terrestrial telescope be used for observing astronomical objects ?

Answer» Yes, the final image will be erect w.r.t. the object. It may be less bright as compared to the image in the astronomical telescope, because of absorption of some light by erecting lens.
833.

Which of the following form(s) a virtual and erect image for all position of the object?A. Concave lensB. Concave mirrorC. Convex mirrorD. Both (a) and (c )

Answer» Correct Answer - D
Concave lens and convex mirror are diverging in nature. They forms virtual and erect images.
834.

When we see an object, image formed on the retina is (i) real (ii) virtual (iii) erect (iv) invertedA. real and invertedB. virtual and erectC. real and erectD. virtual and inverted

Answer» Correct Answer - A
(a) image formed on the retina is real and inverted.
835.

If an object is placed 10 cm infront of a concave mirror of focal length 20cm, the image will beA. Diminished, upright, virtualB. Enlarged, upright, virtualC. Diminished, inverted, realD. Enlarged, upright, real

Answer» Correct Answer - b
836.

Which of the following form(s) a virtual and erect image for all positions of the objectA. Convex lensB. Concave lensC. Convex mirrorD. Concave mirror

Answer» Correct Answer - bc
837.

An object cm 1 tall is placed cm 4 infront of a mirror. In order to produce an upright image of cm 3 height one needs aA. Convex mirror of radius of curvature 12 cmB. Concave mirror of radius of curvature 12 cmC. Concave mirror of radius of curvature 4 cmD. Plane mirror of height 12 cm

Answer» Correct Answer - b
838.

A real object is placed infront of a convex mirror (focal length f). It moves towards the mirror, the image also moves. If `V_(i)=` speed of image and `V_(0)=` speed of the object and u is the distance of object from mirror along principal axis, thenA. `V_(i) le V_(0) " if " |u| lt |F|`B. `V_(i) gt V_(0) " if " |u| gt |F|`C. `V_(i) lt V_(0) " if " |u| gt |F|`D. `V_(i)=V_(0) " if " |u| =|F|`

Answer» Correct Answer - A::C
839.

A convex mirror has a focal length f. A real object is placed at a distance f in front of it from the pole produces an image atA. InfinityB. `f`C. `f//2`D. `2 f`

Answer» Correct Answer - c
840.

A tank is filled with water to a height of `12.5 cm`. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be `9.4 cm`. What is the refractive index of water ? If water is replaced by a liquid of refractive index `1.63` upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?

Answer» Here, real depth `=12.5 cm` , apparent depth `= 9.4 cm , mu = ?`
As `mu = ("real depth")/("apparent depth") :. mu = (12.5)/(9.4) = 1.33`
Now, in the second case, `mu = 1.63`, real depth `= 12. 5 cm` , apparent depth, `y = ?`
`:. 1.63 = (12.5)/(y)`
`y = (12.5)/(1.63) = 7.67 cm`.
`:.` Distance through which microscope has to be moved up `= 9.4 - 7.67 = 1.73 cm`.
841.

The apparent depth of a needle laying at the bottom of the tank, which is filled with water of refractive index `1.33` to a height of `12.5` cm is measured by a microscope to be `9.4 cm`. If water is replaced by a liquid of refractive index `1.63` upto the same height. What distance would the microscope have to be moved to focus on the needle again ?A. `1.73 cm`B. `2.13 cm`C. `1.5 cm`D. `2.9 cm`

Answer» Correct Answer - A
Apparent depth `= ("Real depth")/(.^(@)mu_(l))`
Here, Real depth `= 12.5 cm` and `.^(a)mu_(l) = 1.63`
`:.` Apparent depth `= (12.5)/(1.63) = 7.67 cm`
Now the microsphere will have to shift from its initial position to focus `9.4 cm` depth object to focus `7.67 cm` depth object.
Shift distance `= 9.4 - 7.67 = 1.73 cm`
842.

Light incident normally on a plane mirror attached to a galvenometer coil reflects backward as shown in figure. A current in the coil produes a deflection of `3.5^(@)` if the mirror. The displacement of the reflected spot of light on a screen placed `1.0 m` away is A. `27.5 m`B. `48.9 cm`C. `24.5 cm`D. `12.2 m`

Answer» Correct Answer - C
Angle of deflection is `theta = 3.5^(@)`, Distance between the screen and the mirror is `= 2.0 m`
The reflected rays gets deflected by an amount twice the angle of deflection , i.e., `2theta = 7.0^(@) :. tan 2 theta = d/2`
`rArr d = 2 xx tan 7^(@)= 2 xx 0.1227 = 0.245 m = 24.5 cm`
843.

A rays of light is incident on a thick slab of glass of thickness t as shown in figure. The emergent ray is parallel to the incident ray but displaced sideways by a distance d. If the angles are small then d is A. `t(1+(i)/(r))`B. `rt(1-(i)/(r))`C. `it(1-(r)/(i))`D. `t(1+(r)/(i))`

Answer» Correct Answer - C
Lateral shift, ` d = (t)/(cosr) sin (i-r)`
For small angles `sin(i-r) ~~ i - r`, `cosr~~1`
`d = t(i-r), d =` it `[1- (r)/(i)]`
844.

Assertion : A beam of the white light shows no dispersion on emerging from a glass slab. Reason : Dispersion in a glass slab is zero.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true and reason is not the correct explanation of assertion.C. If assertion is true but reason is false.D. If both assertion and reason are false.

Answer» Correct Answer - C
Velocity of light is different for different mediums. On entering the glass slab, the constituents colours of white light undergo different amount of deviation. Thus there is dispersion inside the glass slab. After refraction at the two parallel to the direction of incidence of white light on the slab, but is laterally displaced. The beam of light has serveral rays, each of which is dispared by the glass slab. These rays combine again and form white light and emerges out as white light.
845.

White light is incident normally on a glass slab. Inside the glass slab,A. red light travels faster than other coloursB. violet light travels faster than other coloursC. yellow light travels faster than other coloursD. all colours travels with the same speed.

Answer» Correct Answer - A
846.

Assertion : Angle of deviation depends on the angle of prism. Reason : For thin prism, `del = (mu - 1) - A`.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true and reason is not the correct explanation of assertion.C. If assertion is true but reason is false.D. If both assertion and reason are false.

Answer» Correct Answer - A
For a thini prism, the relation between angle of deviation, `del`, angle of prism A and refractive index `mu` is
`del = (mu - 1)A`
847.

A small angled prism `(mu = 1.62)` gives a deviation of `4.8`. Calculate the angle of prism.A. `5^(@)`B. `6.36^(@)`C. `3^(@)`D. `7.74^(@)`

Answer» Correct Answer - D
Here, `mu = 1.62, del = 4.8^(@)`
`del = (mu-1) A` or `A = (delta)/((mu-1))= (4.8)/((1.62 - 1)) = 7.74^(@)`
848.

Which of the following colours of white light deviated most when passes through a prism ?A. Red lightB. Violet lightC. Yellow lightD. Both (a) and (b)

Answer» Correct Answer - B
The bending of red component of white light is least while most for the violet component.
849.

The angle of minimum deviation for prism of angle `pi//3 is pi//6`. Calculate the velocity of light in the material of the prism if the velocity of light in vacuum is `3 xx 10^8 ms^-1`.A. `2.12 xx 10^(8) ms^(-1)`B. `1.12 xx 10^(8) ms^(-1)`C. `4.12 xx 10^(8) ms^(-1)`D. `5.12 xx 10^(8) m s^(-1)`

Answer» Correct Answer - A
Using, `mu = (sin(A+delta_(m))//2)/(sinA//2)`
Here, `A = (pi)/(3) = 60^(@), delta_(m)= (pi)/(6) = 30^(@), c = 3 xx 10^(8) m s^(-1)`
`:. Mu = (sin(60^(@) + 30^(@))//2)/(sin60^(@)//2) = (0.7071)/(0.50)= 1.414`
Therefore, `v = c/mu = (3 xx 10^(8))/(1.414)` or `v = 2.12 xx 10^(8) ms^(-1)`
850.

A ray of light is incident at small angle I on the surface of prism of small angle A and emerges normally from the oppsite surface. If the refractive index of the material of the prism is mu, the angle of incidence is nearly equal toA. `A//mu`B. `A//(2mu)`C. `muA`D. `muA//2`

Answer» Correct Answer - C