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:

  1. 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,

$$ \begin{aligned} P & =-\frac{3}{2} & \Big[P=\frac{1}{F(m)}\Big] \\ & =-1.5 & \end{aligned} $$



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