Question #111043
[img]https://upload.cc/i1/2020/04/20/ub5KAU.jpg[/img]



question in picture .R=4
1
Expert's answer
2020-04-28T09:47:55-0400

As per the given question,



Let the focal length of the lens 1 is f1 and focal length of the lens 2 is f2,

R1=8cm,R2=2cm,R1=,R2=(10+R)R_1=8cm, R_2=2cm, R_1'=\infty , R_2'=(10+R)

R=4

a) We know that

1f1=1R1+1R2\dfrac{1}{f_1}=\dfrac{1}{R_1}+\dfrac{1}{R_2}

1f1=1812=58\dfrac{1}{f_1}=\dfrac{1}{-8}-\dfrac{1}{2}=\dfrac{-5}{8}

So, f1=85=1.6cmf_1=\dfrac{-8}{5}=-1.6cm

Similarly,

1f2=1R1+1R2=1+114\dfrac{1}{f_2}=\dfrac{1}{R_1'}+\dfrac{1}{R_2'}=\dfrac{1}{\infty}+\dfrac{1}{-14}

Hence focal length of the lens 2 will be f2=14cmf_2=-14cm

b) Net focal length fnetf_{net}

1fnet=1f1+1f2+df1f2\dfrac{1}{f_{net}}=\dfrac{1}{f_1}+\dfrac{1}{f_2}+\dfrac{d}{f_1f_2}

Now, substituting the values,

1fnet=11.6+114+18121.6×14\dfrac{1}{f_{net}}=\dfrac{1}{-1.6}+\dfrac{1}{-14}+\dfrac{18-12}{1.6\times 14}

1fnet=(14+1.661.6×14)=9.622.4=37\dfrac{1}{f_{net}}=-(\dfrac{14+1.6-6}{1.6\times 14})=\dfrac{-9.6}{22.4}=\dfrac{-3}{7}

fnet=73cmf_{net}=\dfrac{-7}{3}cm

Object is at origin, so u =12cm, let the final image is at v,

v=fnetufnet+u=73×(12)1273=8443=1.95cmv=\dfrac{f_{net}u}{f_{net}+u}=\dfrac{\dfrac{-7}{3}\times(-12)}{-12-\dfrac{-7}{3}}=\dfrac{84}{-43}=-1.95cm

c) M=v/u=1.95/(12)=0.1625M=v/u=-1.95/(-12)=0.1625



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