You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird's image?
To determine the distance at which you must set the focus of the camera lens, you need to understand the concept of image formation through a plane mirror.
First, let's consider the diagram. You have a bird sitting on a tree branch in front of a plane mirror. The light from the bird reflects off the mirror and reaches your camera.
When light rays hit a plane mirror, they obey the law of reflection, which states that the angle of incidence is equal to the angle of reflection, and the incident ray, the reflected ray, and the normal to the mirror at the point of incidence are all in the same plane.
In this scenario, the light rays from the bird will strike the mirror and reflect back towards your camera. To capture a sharp picture of the bird's image, you need to adjust the camera's focus at a distance that enables the reflected light rays to converge to a point on the camera's image sensor.
To determine this distance, consider the following steps:
1. Start by drawing a diagram to visualize the setup. Draw a line from the bird's position to the point of reflection on the mirror, and then extend that line to the point where it intersects the camera lens.
2. Based on the law of reflection, the angle of incidence equals the angle of reflection. So, draw a normal line at the point of incidence on the mirror, which will be the perpendicular bisector of the incident ray.
3. Now, draw a line from the point on the mirror where the light ray reflects to the camera lens. The angle between this line and the normal line represents the angle of incidence, and it will help us determine the distance at which to set the focus.
4. Measure the distance between the point of intersection on the camera lens and the image sensor. This distance represents the focus distance.
5. By using trigonometry, you can find the focus distance. You'll need to know the angle of incidence and the distance between the point of reflection on the mirror and the camera lens. With these values, you can use tangent or other trigonometric functions to calculate the focus distance.
Remember that the angle of incidence can be found by using the properties of similar triangles, as the triangle formed by the bird's position, the point of reflection, and the camera lens is similar to the triangle formed by the point of reflection, the point of intersection with the mirror, and the point of intersection with the camera lens.
By following these steps and determining the focus distance using trigonometry, you can set the camera lens focus at the appropriate distance to capture a sharp picture of the bird's image reflected by the plane mirror.