(a) Prove that to obtain a real image on a screen with the help of a convex lens, the minimum distance between

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Q. (a) Prove that to obtain a real image on a screen with the help of a convex lens, the minimum distance between the object and the screen should be four times the focal length of the lens.

(b) Two convex lenses having focal lengths f1 and f2 are placed in contact on same axis. Find the equivalent focal length of the combination.

(c) A thin prism of angle 6° creates deviation of 3°. Determine the refractive index of the material of the prism. (2+2+1) OR

(a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen in front of a double slit. Hence, obtain the expression for the fringe width.

(b) Draw the intensity distribution curve observed on the screen due to diffraction. ((1+2)+2)

West Bengal WbchseWest Bengal HS (WBCHSE) Board 2025Subjective· 5mImportance★★★★★

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A convex lens needs at least D = 4f between a real object and its real image on a screen (minimum at u = v = 2f); two thin lenses in contact combine as 1/F = 1/f₁+1/f₂; a thin-prism deviation formula gives μ directly.

(a) Minimum object–screen distance = 4f: Let D be the fixed distance between the object and the screen, with the lens somewhere between them, u = object distance, v = image distance (real image), $u+v=D$ (magnitudes) and the lens formula $\dfrac1v-\dfrac1{-u}=\dfrac1f$ , i.e. $\dfrac1v+\dfrac1u=\dfrac1f$ .

Write $v = D-u$ :

$\dfrac{1}{D-u}+\dfrac1u=\dfrac1f\ \Rightarrow\ u(D-u)=f\,D$

$u^2-Du+fD=0$

For u to be real, the discriminant must be ≥ 0:

$D^2-4fD\ge0\ \Rightarrow\ D\ge4f$

So the minimum value of D (object-to-screen distance) for a real image to form is $D_{min}=4f$ , which occurs when $u=v=2f$ (the two roots of the quadratic coincide).

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Q.(a) Prove that to obtain a real image on a screen with the help of a convex lens, the minimum distance between the object and the screen should be four times the focal length of the lens.

Concept understanding — Displacement Method and Conjugate Points

Q.(a) Prove that to obtain a real image on a screen with the help of a convex lens, the minimum distance between the object and the screen should be four times the focal length of the lens.

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