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1.

Two convex lenses of focal length `f_1` and `f_2` are mounted coaxially separated by a distance. If the power of the combination is zero, the distance between the lenses isA. `|f_1-f_2|`B. `f_1+f_2`C. `(f_1f_2)/(|f_1-f_2|)`D. `(f_1f_2)/(f_1-f_2)`

Answer» Correct Answer - B
`d:` distance between lenses
`(1)/(F)=(1)/(f_1)+(1)/(f_2)-(d)/(f_1f_2)`
`P=(1)/(F)=0`
`(d)/(f_1f_2)=(1)/(f_1)+(1)/(f_2)=(f_2+f_1)/(f_1f_2)`
`d=f_1+f_2`
Discussion
2.

if `mu_2=._au_g=(3)/(2),mu_3=._au_(omega)=(4)/(3)`, magnitude of radii of carvature of lens are 10 cm and 20 cm find focal length of lens if rays are incident from (a) air and (b) water,

Answer» (a) If rays are incident from air side
`mu_1=1,mu_2=``_au_g=(3)/(2),mu_3=``_au_(omega)=(4)/(3),R_1=10cm,R_2=-20cm`
`(mu_3)/(f_2)=(mu_2-mu_2)/(R_1)+(mu_3-mu_2)/(R_2)`
`((4)/(3))/(f_2)=((3)/(2)-1)/(10)+((4)/(3)-(3)/(2))/(-20)=(1)/(20)+(1)/(120)=(7)/(120)`
`(4)/(3f_2)=(7)/(120)impliesf_2=(160)/(7)cm`
(b). If rays are incident from water side
`mu_1=``_au_(omega)=(4)/(3),mu_2=``_au_g=(3)/(2)`
`mu_3=1,R_1=20cm,R_2=-10cm`
`(mu_3)/(f_1)=(mu_2-mu_1)/(R_1)+(mu_3-mu_2)/(R_2)`
`(1)/(f_1)=((3)/(2)-(4)/(3))/(20)+(1-(3)/(2))/(-10)`
`=(1)/(120)+(1)/(20)=(7)/(120)`
`f_1=(120)/(7)cm`
Discussion
3.

A thin lens of focal length + 12 cm is immersed in water `(mu = 1.33).` What is its new focal length ?

Answer» `f_a=12cm`,`_au_g=(3)/(2)`,`._au_(omega)=(4)/(3)`
`(1)/(f_a)=(._au_g-1)((1)/(R_1)-(1)/(R_2))` …(i)
`(1)/(f_(omega))=(._(omega)u_g-1)((1)/(R_1)-(1)/(R_2))` ..(ii)
`(i)//(ii)`
`(f_(omega))/(f_a)=((._au_(g)-1))/((._(omega)u_(g)-1))=((._au_(g)-1))/(((._au_(g))/(._au_(omega))-1))=((3//2)-1)/(((3//2)/(4//3)-1))=(((1)/(2)))/(((1)/(8)))=4`
`f_(omega)=4f_(a)=4xx12=48cm`
Discussion
4.

A lens forms a sharp image on a screen. On inserting a parallel sided glass slab between the lens and the screen, it is found necessary to move the screen a distance `d` away the lens in order for the image to be sharp again. If the refractive index of the material of the slab is `mu`, the thickness of the slab isA. `mud`B. `(d)/(mu)`C. `(mu-1)/(mu)d`D. `(mud)/(mu-1)`

Answer» Correct Answer - D
Shift`=t(1-(1)/(mu))=d`
`t=(d)/((1-(1)/(mu)))=(mud)/((mu-1))`
Discussion
5.

A real image of an object is formed by a conex lens at the bottom of an empty beaker. The beaker is now filled with a liquid of refractive index 1.4 to a depth of 7 cm. In order to get the image again at the bottom the beaker shoud be movedA. downward by 2 cmB. upward by 2 cmC. downward by 3 cmD. upward by 3 cm

Answer» Correct Answer - A
Shift by water tank
`7(1-(1)/(1.4))=2cm` away from lens
Discussion
6.

A thin convergent glass lens `(mu_g=1.5)` has a power of `+5.0D.` When this lens is immersed in a liquid of refractive index `mu_1,` it acts as a divergent lens of focal length `100 cm.` The value of `mu_1` isA. `(4)/(3)`B. `(3)/(2)`C. `(5)/(3)`D. `2`

Answer» Correct Answer - C
`(1)/(f_a)=((3)/(2)-1)((1)/(R_1)-(1)/(R_2))` … (i)
`(1)/(f_l)=((3//2)/(._amu_l)-1)((1)/(R_1)-(1)/(R_2))`
(i)/(ii)
`(f_l)/(f_a)=((3//2-1))/(((3//2)/(._amu_l)-1))`
`f_(1)=(100)/(P)=(100)/(5)=20cm`
`f_(l)=-100cm`
`(-100)/(20)=(1//2)/((3/(2_(a)mu_(l))-1))`
`(3)/(2_(a)mu_(l))-1=-(1)/(10)implies(3)/(2_(a)mu_(l))=(9)/(10)`
`._amu_l=(15)/(9)=(5)/(3)`
Discussion
7.

Focal length of a convex lense in air is `10cm`. Find its focal length in water. Given that `mu_g=3//2` and `mu_w=4//3`.A. 2.5 cmB. 5 cmC. 20 cmD. 40 cm

Answer» Correct Answer - D
`(1)/(f_1)=(._amu_g-1)((1)/(R_1)-(1)/(R_2))` …(i)
`(1)/(f_(omega))=(._(omega)mu_g-1)((1)/(R_1)-(1)/(R_2))` ….(ii)
`f_(omega)/(f_(a))=((._amu_(g)-1))/((._omegamu_(g)-1))=((._amu_(g)-1))/(((._amu_(g))/(._amu_omega)-1))`
`(f_(omega))/(10)=(((3)/(2)-1))/(((3//2)/(4//3)-1))=4impliesf_(omega)=40cm`
Discussion
8.

A point object `O` is kept at a distance `OP=u` The radius of curvature of the spherical surface APB is `CP=R` The refractive index of the media are `n_1` and `n_2` which are as shown in the diagram . Then, (A) if `n_1gtn_2`, image is virtual for all values of u (B) if `n_2=2n_1` image is virtual when `Rgtu` (C) The image is real for all values of `u`, `n_1` and `n_2` here, the correct statements is/areA. only (B)B. both (A) and (B)C. only (A)D. (A),(B) and (C)

Answer» Correct Answer - B
`(n_2)/(v)-(n_1)/(u)=(n_2-n_1)/(R)`
`u=-u,R=R`
`(n_2)/(v)-(n_1)/(-u)=(n_2-n_1)/(R)`
`(n_2)/(v)=(n_2-n_1)/(R)-(n_1)/(u)`
if `n_1gtn_2,(n_2)/(v)=-veimpliesv=-ve` (A) is O.K.
if `n_1=2n_1,(n_2)/(v)=(n_1)/(R)-(n_1)/(u)=-ve`, if `Rgtu`.
(B) is O.K.
Discussion
9.

The graps shows the variation of magnification `m` produced by as convex lens with the image distance `v`. The focal length of the lens isA. `(b)/(c)`B. `(c)/(b)`C. `a`D. `a,(b)/(c)`

Answer» Correct Answer - D
For lens `(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(v)-(1)/(-u)=(1)/(f)`
`(v)/(v)+(v)/(u)=(v)/(f)implies(v)/(u)=(v)/(f)-1`
`m=(v)/(f)-1impliesu=(1)/(f)x-1`
Comparing with `y=Mx+C`
Slope `M=(1)/(f)=(b)/(c)impliesf=(c)/(b)`
Discussion
10.

A convex lens of focal length 40 cm a concave lens of focal length 40 and a concave lens of focal length 15 cm are placed in contact. The power of this combination of are placed in contact. The power of this combination in diopters isA. `+1.5`B. `-1.5`C. `+6.67`D. `-6.67`

Answer» Correct Answer - D
`(1)/(F)=(1)/(f_1)+(1)/(f_2)+(1)/(f_3)`
`=(1)/(40)+(1)/(-40)+(1)/(-15)=-(1)/(15)`
`P=(100)/(F(cm))=-(100)/(15)=-(20)/(3)=-6.67D`
Discussion
11.

Two thin lenses of powers `2D` and `3D` are placed in contact. An object is placed at a distance of 30 cm from the combination The distance in cm of the image from the combination isA. 30B. 40C. 50D. 60

Answer» Correct Answer - D
`P=P_1+P_2=5D,F=(100)/(P)=(100)/(5)=20cm`
`(1)/9v-(1)/(-30)=(1)/(20)`
`(1)/(v)=(1)/(20)-(1)/(30)=(1)/(60)impliesv=60cm`
Discussion
12.

A cardsheet divided into squares each of size `1 mm^(2)` is being viewed at a distance of `9 cm` through a magnifying glass (a conerging lens of focal length `10 cm`) held close to the eye. (a) What is the magnification produced by the lenas ? How much is the area of each square to the virtual image ? (b) What is the angular magnification (magnifying power) of the lens ? ( c) Is the magnification in (a) equal to the magnifying power in (b) ? ExplainA. `1cm^2`B. `0.81cm^2`C. `0.27^2`D. `0.60cm^2`

Answer» Correct Answer - A
`u=-9cm,f=10cm`
`(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(v)-(1)/(-9)=(1)/(10)`
`(1)/(v)=(1)/(10)-(1)/(9)=(-1)/(90)`
`v=-90cm`
`m=(v)/(u)=(-90)/(-9)=10`
`(A_i)/(A_O)=m^2implies(A_i)/(I)=(10)^2`
`A_i=100m^2=1cm^2`
Discussion