Question

As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water (μ = 4/3). The height of water is the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ____cm.

Answer 1

Correct Answer: 98

The goal is to find the apparent position of the bulb's image as seen from the mirror. This involves calculating the apparent depth of the bulb in water, then using this information to determine the total distance of the image from the bottom of the tank.

Apparent Depth Calculation:  The real depth of the bulb in the water is 8 cm. The refractive index (μ) of water is 4/3. The apparent depth (da) is given by the formula: da = dr × (1/μ) = 8 × (3/4) = 6 cm

Determine Total Image Distance: Since the mirror is 50 cm above the bottom of the tank, the image will appear as if it is the same distance inside the mirror as the object's apparent depth under the water. The distance from the apparent position to the mirror is (50 cm - 6 cm = 44 cm). The image distance from the mirror by reflection is the same: 44 cm in air.

Calculate Total Distance from Bottom: The total distance from the bottom of the tank to the image is: 8 cm + 44 cm + 44 cm = 96 cm

Conclusion: The distance of the image of the bulb from the bottom of the tank is 96 cm, which is within the provided range (98,98).