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A 35-year-old patent clerk needs glasses of 50-cm focal length to read patent applications that he holds 25 cm from his eyes. Five years later, he notices that while wearing the same glasses, he has to hold the patent applications 40 cm from his eyes to see them clearly.

What should be the focal length of new glasses so that he can read again at 25cm?

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lublana

Answer:

28.57 cm

Explanation:

We are given that

Focal length,[tex]f=50 cm[/tex]

Distance of application from his eyes,s=40 cm

[tex]\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}[/tex]

[tex]\frac{1}{40}+\frac{1}{s'}=\frac{1}{50}[/tex]

[tex]\frac{1}{s'}=\frac{1}{50}-\frac{1}{40}=\frac{4-5}{200}[/tex]

[tex]s'=\frac{200}{-1}=-200 cm[/tex]

s=25 cm

Substitute the values

[tex]\frac{1}{25}-\frac{1}{200}=\frac{1}{f'}[/tex]

[tex]\frac{8-1}{200}=\frac{1}{f'}[/tex]

[tex]\frac{1}{f'}=\frac{7}{200}[/tex]

[tex]f'=\frac{200}{7}=28.57 cm[/tex]

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