Explanation
It is given that,
R1=−3cm
Focal length of concave lens f1=−32
R2=2cm
Focal length of convex lens f2=1cm
Combined focal length is
1f=1f1+1f2
1f=−23+1
1f=13........(1)
The relation between redfractive index and focal length is
1f=(μ−1)[1R1−1R2]
13=(μ−1)[1−3−12]
13=(μ−1)[−56]
μ=35
Total deviation for yellow ray produced
δy=δcy−δfy+δcy
=2δcy−δfy
=2(μcy−1)A−(μ−cy−1)A1
Angular dispersion,
δv−δr=[(μvc−1)A−(μvf−1)A1+(μvc−1)A]
−[(μrc−1)A−(μrf−1)A1+(μr−1)A]
2(μvc−1)A−(μvf−1)A1
For net angular dispersion to be zero,
δr−δr=0
2(μvc−1)A=(μvf−1)A1
If μ, represents the refractive index when a light ray goes from medium i to j, then 2μ1 x 3μ2 x 4μ3 is equal to
A light ray is incident normally on the surface AB of a prism of refracting angle 60∘. If the light ray does not emerge from AC, then find the refractive index of the prism.
Given that,
Diameter d=2m
Wave length λ=5000∘A
Now, minimum angular separation is
Δθ=1.22λd
Δθ=1.22×5000×10−102
Δθ=0.3×10−6rad
Hence, the resolving power is 0.3×10−6rad
Given,
Radius of curvature, R
Refractive index = 1.5
Focal length of lens, f=R(μ−1)=R(1.5−1)=2R
Magnification from mirror
m=hiho=−vu
Whereas
hi= Height of image from principal axis
ho= Height of object from principal axis
u= Object distance
v= Image distance
Angular magnification m=fofe=1505=30
∴tanβtanα=30⇒tanβ=tanα×30
tanβ=(501000×30)=1510=32
tanβ=32⇒tanβ=tan−1(32)
θ=β≃60∘
At what angle will a ray of light be inclined on one face of an equilateral prism, so that the emergen ray may graze the second surface of the prism (μ=2)
Refractive indexes for, glass μg=1.5, water μw=43 and μa=1 .
If f is the focal length of the lens in air then
1fa=(μgμa−1)×(1R1−1R2).........(1)
If f is the focal length of the lens in water then 1fw=(μgμw−1)×(1R1−1R2).........(2)
Divide equation (1) by (2)
1fa1fw=(μgμa−1)(μgμw−1)
fw=(μg−μaμa×μwμg−μw)fa
fw=(1.5−11×4/31.5−4/3)×20=80cm
Hence, focal length in water, fw=80cm
Focal length f=10cm
Refractive index μ1=1.5
Refractive index μ2=1.25
We know that,
1f=(n−1)(1R1−1R2)
110=(1.5−1)(1R1−1R2)....(I)
1f=(1.25−1)(1R1−1R2)....(II)
Now, divided equation (I) by equation (II)
f10=0.50.25
f=20cm
Hence, the focal length is 20 cm
A convex lens produces an image of an object on a screen with a magnification of 12 .When the lens is moved 30 cm away from the object, the magnification of the image is 2.The focal length of the lens is
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