A Plane mirror gives a spots of lights on the screen which is 3 cm from the mirror the screen is Perpendicular to the initial direction of the ray light when the mirror is rotated the spot of the light moves a distance of 4m across the screen calculate the angle of the rotation of the mirror
To solve this problem, we can use similar triangles.
Let's denote the distance of the screen from the mirror as d, the distance the spot of light moves across the screen as x, and the angle of rotation of the mirror as θ.
Since the screen is perpendicular to the initial direction of the ray of light, we can form a right triangle with the distance from the mirror to the spot of light on the screen as the hypotenuse. The distance from the mirror to the screen (d) is one leg of the triangle, and the distance the spot of light moves across the screen (x) is the other leg of the triangle.
Using similar triangles, we have:
d / x = 4m / 3cm
First, let's convert the units of d to centimeters to match the units of x:
d = 3 cm
Now, let's substitute the known values into the equation and solve for x:
3 cm / x = 4m / 3cm
Cross-multiplying:
3 cm * 3 cm = 4m * x
9 cm^2 = 4m * x
Now, let's convert the units of 4m to centimeters:
4m = 4 * 100cm = 400cm
Substituting the value of 4m, we have:
9 cm^2 = 400cm * x
To solve for x, divide both sides of the equation by 400cm:
x = 9 cm^2 / 400cm
x = 0.0225 cm
Now, we can use the distance x and the distance d to find the sine of the angle θ:
sin(θ) = x / d
sin(θ) = 0.0225 cm / 3 cm
sin(θ) ≈ 0.0075
Finally, to find the angle θ, we can take the inverse sine of 0.0075:
θ ≈ sin^(-1)(0.0075)
θ ≈ 0.43 degrees
Therefore, the angle of the rotation of the mirror is approximately 0.43 degrees.