Geometrical OpticsMedium
Question
A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?
Options
A.behaves as concave lens if $\left| f_{\text{convex}\text{~}} \right| > \left| f_{\text{concave}\text{~}} \right|$
B.behaves as concave lens if $\left| f_{\text{convex}\text{~}} \right| < \left| f_{\text{concave}\text{~}} \right|$
C.behaves as convex lens if $\left| f_{\text{convex}\text{~}} \right| > \left| f_{\text{concave}\text{~}} \right|$
D.Focal length of the lens system will change if the position of two lenses are interchanged
Solution
Sol. [Key Concept: $\frac{1}{f} = \frac{1}{f_{1}} - \frac{1}{f_{2}}$; if ${|f}_{convex}| > {|f}_{concave}|$ the net focal length is negative, so the pair acts as a concave lens.]
$\ 1 \rightarrow$ convex lens
$2 \rightarrow$ concave lens
$$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{- f_{2}}:\frac{1}{f_{1}} - \frac{1}{f_{2}} $$for $f_{1} > f_{2}\therefore f < 0$
∴ concave lens.
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