Optics 3 Question 23
23. An eye specialist prescribes spectacles having combination of convex lens of focal length $40 cm$ in contact with a concave lens of focal length $25 cm$. The power of this lens combination in diopters is
(1997, 2M)
(a) +1.5
(b) -1.5
(c) +6.67
(d) -6.67
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Answer:
Correct Answer: 23. (b)
Solution:
- The focal length of combination is given by
$$ \begin{array}{rlr} \frac{1}{F} & =\frac{1}{40}-\frac{1}{25} \quad \Big(\frac{1}{F}=\frac{1}{F _1}+\frac{1}{F _2}\Big) \\ \text { or } \quad F & =-\frac{200}{3} cm \\ & =-\frac{2}{3} m \end{array} $$
$\therefore$ Power of the combination in dioptres,
$$ \begin{aligned} P & =-\frac{3}{2} & \Big[P=\frac{1}{F(m)}\Big] \\ & =-1.5 & \end{aligned} $$
