Question

answer when the photograph of an object is taken by using a pinhole camera the magnification is 0.05. when pinhole camera is moved through a distance 2m towards the object magnification is 0.0625. determine width of pinhole camera

Answer 1

$$\begin{gathered} Theformulaforthediameterofthepinholeisgivenby, \\ d=2\sqrt{v\lambda },whered,vand\lambda arethedimeterofpinhole,diss\tan ceofimagefromthepinhole \\ andwavelengthofyellowlightrespectively. \\ whenpinholeismovedby2mtowardstheobjectthen \\ d=2\sqrt{\left(v+2\right)\lambda } \\ againv/u=0.05 \\ orv=0.05u---\left(1\right) \\ againv+2=0.0625(u-2)----\left(2\right) \\ fromeqns\left(1\right)and\left(2\right), \\ 0.05u+2=0.0625u-1.250 \\ or0.0125u=3.250 \\ oru=\frac{32500}{125}=214m. \\ nowv=0.05\times 214=10.70 \\ therefored=2\sqrt{v\lambda }=2\sqrt{10.7\times 550\times {10}^{-9}}=2\sqrt{588.5}\times {10}^{-5}=2\times 24.2\times {10}^{-5} \\ ord=0.242\times {10}^{-3}m=0.242mm. \end{gathered}$$