A source of light and a screen lie in the same plane, 3 metres in front of a plane mirror, the mirror surface being parallel with the screen. If the mirror is rotated through 10degrees, how far will the patch of light mves across the screen?

The source originally coincides with its reflection on the screen. If the mirror is tilted 10 degrees, the angle of the reflected beam is displaced 20 degrees in the same direction. That would displace it 3.0*tan20 = 1.09 meters on the screen

When a plane mirror is rotated, the angle of incidence and angle of reflection change accordingly, while the position of the object and image remain the same. In this case, the light source is the object and the patch of light on the screen is the image.

To determine how far the patch of light will move across the screen, we need to find the displacement of the image caused by the rotation of the mirror.

Since the mirror is rotated through 10 degrees, the angle of incidence and angle of reflection at the mirror surface will also change by 10 degrees.

Now, let's consider the geometry of the situation. We have a right triangle formed by the light source, the mirror, and the screen. The hypotenuse of this triangle represents the path of light from the source to the mirror to the screen.

Given that the mirror is 3 meters away from the screen, and the mirror is rotated by 10 degrees, we can use trigonometry to find the displacement of the patch of light.

Using the trigonometric function tangent (tan), we can relate the angle of rotation (10 degrees) to the displacement (d) on the screen. The formula is:

tan(theta) = opposite/adjacent

In this case, the opposite side is the displacement (d), and the adjacent side is the distance between the mirror and the screen (3 meters). Plugging in the values, we have:

tan(10 degrees) = d/3

Now, we can solve for the displacement (d) by isolating it:

d = tan(10 degrees) * 3

Using a calculator, the value of tan(10 degrees) is approximately 0.17633. Multiplying this by 3, we get:

d ≈ 0.17633 * 3

d ≈ 0.529 meters

Therefore, the patch of light will move approximately 0.529 meters across the screen due to the rotation of the mirror.

To determine how far the patch of light moves across the screen when the mirror is rotated, we can use the concept of reflection.

Let's break down the problem and go step by step to find a solution:

1. Initially, the source of light and the screen are set up in the same plane, 3 meters in front of the plane mirror. The mirror surface is parallel to the screen.

2. When the mirror is rotated through 10 degrees, it changes the angle of incidence and reflection of light.

3. To calculate how far the patch of light moves across the screen, we need to find the displacement of the reflected light.

4. According to the law of reflection, the angle of incidence and the angle of reflection are equal.

5. Since the mirror is rotated through 10 degrees, the angle of incidence is 10 degrees, and the angle of reflection also becomes 10 degrees.

6. Now, we can use trigonometry to find the displacement of the reflected light. The formula we'll use is:

Distance Moved = 2 * Distance to the Mirror * tan(Angle of Reflection)

Distance to the Mirror = 3 meters (given)

Angle of Reflection = 10 degrees

Distance Moved = 2 * 3 * tan(10)

7. Plugging the values into the formula and calculating:

Distance Moved = 2 * 3 * tan(10)
Distance Moved ≈ 0.35 meters

Therefore, the patch of light moves approximately 0.35 meters across the screen when the mirror is rotated through 10 degrees.