Question:
A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. To what height the image of this fish is raised? (Refractive index of lake water \( n = \frac{4}{3} \))
A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. To what height the image of this fish is raised? (Refractive index of lake water \( n = \frac{4}{3} \))
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When observing an object underwater, the apparent depth is less than the real depth due to the refractive index of water.
Updated On: Apr 22, 2026
- 9 cm
- 12 cm
- 3.8 cm
- 3 cm
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The Correct Option is D
Solution and Explanation
Step 1: Understand the refraction of light in water.
The apparent depth \( d_{\text{apparent}} \) of an object submerged in water is given by the formula: \[ d_{\text{apparent}} = \frac{d_{\text{real}}}{n} \] where: - \( d_{\text{real}} \) is the actual depth of the object, - \( n \) is the refractive index of the water.
Step 2: Apply the formula.
Given that the actual depth \( d_{\text{real}} = 12 \, \text{cm} \) and the refractive index of the water is \( n = \frac{4}{3} \), we substitute these values into the formula: \[ d_{\text{apparent}} = \frac{12}{\frac{4}{3}} \]
Step 3: Simplify the expression.
Simplifying the expression: \[ d_{\text{apparent}} = 12 \times \frac{3}{4} = 9 \, \text{cm} \] Thus, the apparent depth (the height the image is raised) is \( 3 \, \text{cm} \).
The apparent depth \( d_{\text{apparent}} \) of an object submerged in water is given by the formula: \[ d_{\text{apparent}} = \frac{d_{\text{real}}}{n} \] where: - \( d_{\text{real}} \) is the actual depth of the object, - \( n \) is the refractive index of the water.
Step 2: Apply the formula.
Given that the actual depth \( d_{\text{real}} = 12 \, \text{cm} \) and the refractive index of the water is \( n = \frac{4}{3} \), we substitute these values into the formula: \[ d_{\text{apparent}} = \frac{12}{\frac{4}{3}} \]
Step 3: Simplify the expression.
Simplifying the expression: \[ d_{\text{apparent}} = 12 \times \frac{3}{4} = 9 \, \text{cm} \] Thus, the apparent depth (the height the image is raised) is \( 3 \, \text{cm} \).
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