Arrange the focal lengths of the following lenses made of glass in as…

The correct answer is Option (3) → B, D, A, C

Find each focal length separately, using the lens maker’s formula, the lens formula and the magnifier formula. Glass is taken as \( n = 1.5 \), the least distance of distinct vision as \( D = 25 \) cm and the far point of a normal eye at infinity (the usual values).

(A) A convex lens, each face having radius of curvature \( 1 \) m — \( R_1 = +1 \) m and \( R_2 = -1 \) m:

    \( \displaystyle \frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = (1.5 - 1)\left(\frac{1}{1} + \frac{1}{1}\right) = 1\,\mathrm{m^{-1}} \)

    \( f_A = 1\,\mathrm{m} = 100\,\mathrm{cm} \)

(B) When image is formed at \( 40 \) cm from a lens with linear magnification \( -1 \) — a magnification of \( -1 \) means a real, inverted image of the same size, which forms when object and image are both at 2f:

    \( v = 2f = 40\,\mathrm{cm} \Rightarrow f_B = 20\,\mathrm{cm} \)

(C) Lens of power \( 0.1 \) D — \( P = 1/f \) with f in metres:

    \( f_C = 1/P = 1/0.1 = 10\,\mathrm{m} = 1000\,\mathrm{cm} \)

(D) When image is at a far point and angular magnification is \( 1 \) — a magnifier with the image at the far point (infinity) has angular magnification \( m = D/f \):

    \( m = D/f = 1 \Rightarrow f_D = D = 25\,\mathrm{cm} \)

    \( f_B\ (20\,\mathrm{cm}) \lt f_D\ (25\,\mathrm{cm}) \lt f_A\ (100\,\mathrm{cm}) \lt f_C\ (1000\,\mathrm{cm}) \)

The ascending order is B, D, A, C.