Example questions from refraction through curved surfaces

Example questions

1 1) Two converging lenses are to be placed in the path of parallel rays so that the rays remain parallel after passing through both lenses. How should the lenses be arranged? Explain with a neat ray diagram.

ANS:

i) A parallel beam of light rays will converge on focal point of the lens after refraction.

ii) Light rays passes through the focal point will parallel to principal axis after re-fraction.

iii) So the two lenses are arranged on a common principal axis such that their focal points coincide with each other, then the rays remain parallel after passing through both lenses.

2 2) The focal length of a converging lens is 20cm. An object is 60cm from the lens. Where will the image be formed and what kind of image is it?

ANS: Given, f=20 cm

U=-60cm

Lens formula

1/f=1/v-1/u

1/20=1/v-(1/-60)

1/20=1/v+1/60

1/v=1/20-1/60

1/v= (3-1)/60 [L.C.M]

1/v=2/60

1/v=1/30

Therefore v=30 cm

3 3) A double convex lens has two surfaces of equal radii ‘R’ and refractive index n = 1.5. Find the focal length ‘f’.

ANS: Given

Radius of curvature =R

focal length =f

Refractive index, μ=1.5

From lens maker's formula

f1=(μ−1)[1/R₁_-1/R₂]

f1=(1.5−1)[1/R+1/R]

=0.5×2/R

1/f=1/R

f=R

Convex lens made with different materials

A convex lens is made up of three different materials as shown in the figure. How many of images does it form?

ANS: The answer is very simple number of images formed by a lens is equal to the number of different materials used to make the lens.

So, in the above example the number of images formed are three.

5) Find the radii of curvature of a convexo –concave convergent lens made of glass with refractive index n=1.5 having focal length of 24cm. One of the radii of curvature is double the other.

thank you

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