An image formed on a screen is three times the size of the object. The object and screen are 80cm apart when the image is sharply focussed.
- State which type of lens is used.
- Calculate focal length of the lens.
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- The image here can be taken on a screen. This means that the image is real. Further, we know that only convex lens forms a real image therefore, a convex lens has been used here.
- Magnification (m) = 3
Image distance (v) = ?
Focal length (f) = ?
Distance between image and object (v + u) = 80cm
v = 80 - u
We know that:
$\text{m}=\frac{\text{v}}{\text{u}}$
Or $3=\frac{80-\text{u}}{\text{u}}$
Or $3\text{u}=80-\text{u}$
Or $4\text{u}=80$
$\text{u}=20\text{cm}$
Thus, $\text{v}=80-\text{u}$
$=80-20=60\text{cm}$
Putting these values in lens formula, we get,
$\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{60}-\frac{1}{-20}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1+3}{60}=\frac{1}{\text{f}}$
$\Rightarrow\text{f}=\frac{60}{4}=15\text{cm}$
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