Question
Download Solution PDFA needle of height 4 cm is placed at a distance of 45 cm in front of concave lens of focal length 30 cm. The height of the image of the needle will be:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 1.6cm.
Given:
\(u=-45cm,f=-30cm\)
\(hi=4cm\) of a needle placed in a concave lens.
Formula:
Lens formula: \({1 \over f}={1 \over v}-{1 \over u}\)
Calculations:
\({1 \over -30}={1 \over v}-{1 \over -45}\)
\({ 1 \over v}=-({1\over 45}+{1\over30})\)
\({1 \over v}=-{45+30\over1350}=-{75\over1350}=-{1\over18}\)
Therefore, \(v=-18cm \) for a concave lens.
Thus we have the height of needle is:
\({hi\over ho}={v\over u}\)
\(hi={v*ho\over u}\)
\(hi={-18*4\over-45}={72\over45}=1.6cm\)
Therefore, the height of the image formed by the needle is 1.6cm.
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