Question

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is(a) –25 cm(b) –50 cm(c) 50 cm(d) –20 cm

Answer 1

Answer:

Explanation:

ug = 15

uoil = 17

R = 20cm

From len's maker's formula for the piano convex lens -

= 1/f = (u-1)(1-R1-1/R2)

where R1 = r and R2 for plane surface = ∞

= 1/flens = (15-1)(1/R-0)

= 1/flens = 0.5/R

The focal length of concave lens formed by the oil -

= 1/fconcave = (17-1)(-1/R-1/R)

= -0.7×2/R = -14/R

Thus, now we have two concave surfaces

= 1/feq = 2×1/f+1/f

= 2×0.5+(-14/R)

= 1/R-14/R = -0.4/R

Therefore,

feq = -R/0.4 = -20/0.4

= -50cm

Thus, the focal length of the combination is -50cm

Answer 2

Answer:

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