A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.
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f = -15 cm, v = -10 cm Using lens formula, we have$\frac{1}{\text{f}}=\frac{1}{\text{v}}-\frac{1}{\text{u}}$
$\Rightarrow \ \frac{1}{\text{u}}=\frac{1}{\text{v}}-\frac{1}{\text{f}}$
$\frac{1}{\text{u}}=\frac{1}{-10}-\frac{1}{-15}=\frac{-5}{150}$
$\text{u}=\frac{150}{-5}=-30 \ \text{cm}$
Therefore, the object is placed at 30 cm from the lens. The ray diagram is given as follows:
$\Rightarrow \ \frac{1}{\text{u}}=\frac{1}{\text{v}}-\frac{1}{\text{f}}$
$\frac{1}{\text{u}}=\frac{1}{-10}-\frac{1}{-15}=\frac{-5}{150}$
$\text{u}=\frac{150}{-5}=-30 \ \text{cm}$
Therefore, the object is placed at 30 cm from the lens. The ray diagram is given as follows:
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