A concave mirror is placed at the bottom of an empty tank with face upwards and axis vertical When sunlight falls normally on the mirror it is focused at the distance of 32cm from the mirror If the tank filled with water upto a height of 20cm then the sunlight will now focussed at

To determine where the sunlight will be focused when the concave mirror is submerged in water, we need to consider how light behaves when it passes from one medium to another. In this case, we have sunlight traveling through air and then entering water before reflecting off the mirror. The key concept here is the change in the effective focal length of the mirror due to the refraction of light in water.

Understanding Focal Length in Different Mediums

The focal length of a concave mirror is determined by its curvature and is given by the formula:

f = R/2

where f is the focal length and R is the radius of curvature. When light travels from air (with a refractive index of approximately 1) into water (with a refractive index of about 1.33), the effective focal length of the mirror changes. This is due to the fact that light travels slower in water than in air.

Calculating the New Focal Length

The relationship between the focal lengths in different mediums can be expressed as:

f' = f/n

where f' is the new focal length in the water, f is the original focal length in air, and n is the refractive index of the medium (water in this case).

Given that the original focal length f is 32 cm, we can substitute the values:

• f = 32 cm
• n = 1.33

Now, substituting these values into the formula:

f' = 32 cm / 1.33 ≈ 24.06 cm

Determining the Focus Point in Water

Since the tank is filled with water to a height of 20 cm, we need to consider the position of the focus relative to the water surface. The new focal point of approximately 24.06 cm is measured from the mirror's surface. However, since the mirror is at the bottom of the tank, we need to account for the water height.

To find the position of the focus above the water surface, we subtract the height of the water from the new focal length:

Position of focus above water = f' - height of water

Substituting the values:

Position of focus above water = 24.06 cm - 20 cm = 4.06 cm

Final Result

Thus, when sunlight falls normally on the concave mirror submerged in water, the sunlight will be focused at approximately 4.06 cm above the water surface. This demonstrates how the refractive properties of water affect the focal point of the mirror, illustrating the fascinating interplay between optics and fluid dynamics.

To understand how the focus of sunlight changes when a concave mirror is placed in water, we need to consider the principles of optics, particularly how light behaves when it travels through different mediums. In your scenario, the concave mirror focuses sunlight at a distance of 32 cm when it is in air. When the tank is filled with water up to a height of 20 cm, the effective focal length of the mirror changes due to the refraction of light.

The Basics of Refraction

Refraction occurs when light passes from one medium to another, causing it to change speed and direction. The degree of bending depends on the indices of refraction of the two media involved. For air, the index of refraction is approximately 1.00, while for water, it is about 1.33.

Calculating the New Focal Length

The focal length of a concave mirror in air is given as 32 cm. When the mirror is submerged in water, we can use the formula for the effective focal length (f') in a medium:

• f' = f / n

Here, f is the original focal length in air, and n is the refractive index of the medium (water in this case). So, substituting the values:

• f' = 32 cm / 1.33

Calculating this gives:

• f' ≈ 24.06 cm

Understanding the Impact of Water Depth

Since the water fills the tank up to 20 cm, we need to consider how this affects the focus of the sunlight. The sunlight will still be focused at the new effective focal length of approximately 24.06 cm from the mirror's surface. However, since the mirror is submerged, we must account for the distance from the water's surface to the mirror.

Given that the mirror is 20 cm below the water's surface, the actual distance from the water's surface to the focal point will be:

• Distance from water surface to mirror = 20 cm
• Effective focal length in water = 24.06 cm

To find the distance from the water surface to the point where sunlight is focused, we can subtract the depth of the water from the effective focal length:

• Focal point above water surface = 24.06 cm - 20 cm = 4.06 cm

Final Result

Thus, when the tank is filled with water up to a height of 20 cm, the sunlight will be focused at approximately 4.06 cm above the water's surface. This demonstrates how the medium through which light travels can significantly alter its behavior and the resulting focal point.