MHT CET · Physics · Ray Optics
In a compound microscope, let ' \(u_0\) ' and ' \(v_0\) ' be the object distance and image distance respectively. The objective of focal length ' \(f_0\) ' magnifies a tiny object into a real, inverted image. The linear magnification of the objective is
- A \(\frac{f_0+u_0}{u_0 f_0}\)
- B \(\frac{f_0}{f_0+u_0}\)
- C \(\frac{u_0}{u_0 f_0+1}\)
- D \(\frac{u_0 f_0}{f_0+u_0}\)
Answer & Solution
Correct Answer
(B) \(\frac{f_0}{f_0+u_0}\)
Step-by-step Solution
Detailed explanation
Using lens formula:
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)
And definition of magnification,
\(m=\frac{v}{u}\)
Multiply lens formula with \(u\),
\(\left(\frac{u}{v}\right)-1=\frac{u}{f}\)
\(\left(\frac{1}{m}\right)-1=\frac{u}{f}\)
\(m=\frac{f}{(u+f)}\)
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)
And definition of magnification,
\(m=\frac{v}{u}\)
Multiply lens formula with \(u\),
\(\left(\frac{u}{v}\right)-1=\frac{u}{f}\)
\(\left(\frac{1}{m}\right)-1=\frac{u}{f}\)
\(m=\frac{f}{(u+f)}\)
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