Question

An object of height 6 cm is placed perpendicular to the princapal axis of a concave lens of focal length 5cm. Use the lens formula to determine the Position, size and nature of the image if the distance from the lens is 10cm.​

Answer 1

$\large{\red{\bold{\underline{Given:}}}}$

(i) f (Focal Length) = -5cm

(ii) u (Object Distance) = -10cm

(iii) h (Object height) = 6cm

$\large{\green{\bold{\underline{To \: Calculate:}}}}$

(i) v (image distance) = ????

(ii) h' (Size of the image) = ???

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

$\sf \: \frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$\large{\red{\bold{\underline{Calculation:}}}}$

$\rightarrow \sf \: \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \\ \\ \rightarrow \sf \: \frac{1}{v} = - \frac{1}{5} + ( - \frac{1}{10} ) \\ \\ \rightarrow \sf \: \frac{1}{v} = - \frac{1}{5} - \frac{1}{10} \\ \\ \rightarrow \sf \: \frac{1}{v} = \frac{ - 1 \times 2 - 1}{10} \\ \\ \rightarrow \sf \: \frac{1}{v} = \frac{ - 3}{10} \\ \\ \rightarrow \sf \: v = - 3.33cm$

$\large{\pink{\bold{\underline{Now:}}}}$

As per our information

$\sf \: \frac{Size \: of \: the \: Image}{Size \: of \: the \: object} = + \frac{v}{u}$

$\large{\green{\bold{\underline{On \: putting \: all \: the \: values:}}}}$

$\rightarrow \: \sf \: \frac{h'}{h} = \frac{ - 3.3}{ - 10} \\ \\ \rightarrow \: \sf \: \frac{h'}{6} = \frac{ \cancel- 3.3}{ \cancel- 10} \\ \\ \rightarrow \: \sf \: \frac{h'}{6} = \frac{3.3}{10} \\ \\ \rightarrow \: \sf \: h' = \frac{6 \times 3.3}{10} \\ \\ \rightarrow \: \sf \: h' = \frac{19.8}{10} \\ \\ \rightarrow \: \sf \: h' = 1.98$

$\large{\pink{\bold{\underline{Hence:}}}}$

Size of the image is 1.98cm.

$\large{\orange{\bold{\underline{Related \: Information:}}}}$

$\rightarrow \: \sf \: Always \: virtual \: image \: will \: be \:formed \: by \\ \sf \: concave \: lens. \\ \\ \rightarrow \: \sf \: Image \: will \: be \: erect. \\ \\ \rightarrow \: \sf \: Image \: will \: be \: formed \: always \: on \: the \: same \\ \sf \: side \: of \: the \: object.$

Answer 2

Explanation:

1.98cm is the correct answer