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Physics Question on Ray optics and optical instruments

A rod of length 2cm2 \,cm makes an angle 2π3\frac{2 \pi}{3} rad with the principal axis of a thin convex lens The lens has a focal length of 10cm10\, cm and is placed at a distance of 403cm\frac{40}{3} cm from the object as shown in the figure The height of the image is 30313cm\frac{30 \sqrt{3}}{13} cm and the angle made by it with respect to the principal axis is αrad\alpha rad The value of α\alpha is πnrad\frac{\pi}{n} rad, where nn is ___

Answer

Answer: 6