Question

An object is 15cm from the surface of a reflective spherical Christmas tree ornament 6cm in diameter what are the magnification and position of the image?

Answer 1

$\huge{\mathfrak{\blue{\underline{\underline{Solution:-}}}}}$

${\mathtt{\underline{Given;-}}}$

$\sf{u=-15\;cm}$

$\sf{Diameter\;of\;spherical\;lens=6cm}$

$\sf{Radius=3cm}$

$\sf{Focal\;length = 1.5cm}$

$\sf{By\;mirror\;formula,}$

$\sf{\frac{1}{v}+\frac{1}{u}=\frac{1}{f}}$

$\sf{\frac{1}{v}-\frac{1}{15}=\frac{1}{1.5}}$

$\sf{\frac{1}{v} =\frac{1}{1.5}+\frac{1}{15}}$

$\sf{\frac{1}{v} =\frac{11}{15}}$

${\boxed{\boxed{\sf{\red{v=\frac{15}{11}}}}}}$

$\sf{By\;magnification\;formula,}$

$\sf{m=\frac{v}{u}}$

$\sf{\implies \frac{\frac{15}{11}}{15}}$

$\sf{m = \frac{1}{11} = 0.09}$

${\boxed{\boxed{\sf{\red{So,\;m=0.09\;cm}}}}}$