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(i) Draw a ray diagram to show the image formation by a combination of two thin convex lenses in contact. Obtain the expression for the power of this combination in terms of the focal lengths of the lenses.

(ii) A ray of light passing from air through an equilateral glass prism undergoes minimum deviation when the angle of incidence is \(\frac{3}{4}\)th of the angle of prism. calculate the speed of light in the prism.

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(i)

 

Two thin lenses, of focal length f1 and f2 are kept in contact. Let O be the position of object Let u be the object distance. The distance of the image (which is at I1) for the first lens is v1.

This image serves as object for the second lens. let the final image be at I.

We than have.

\(\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u}\)

\(\frac{1}{f_2}=\frac{1}{v}-\frac{1}{v_1}\)

Adding, we get

\(\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

\(∴\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\)

∴ P = P1 + P2

(ii) At minimum deviation

\(r=\frac{A}{2}\) = 30°

We are given that

\(i=\frac{3}{4}A=45°\)

\(∴μ=\frac{sin\,45°}{sin\,30°}=√2\)

∴ Speed of light in the prism = \(\frac{c}{√2}\)

(≅ 2.1 × 108 ms-1)

[Award ½ marks if the student writes the formula: \(μ=\frac{sin(A+δ_m)/2}{sin(A/2)}\) but does not do any calculations.]

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