| Aim | The aim of the experiment is to find the focal length of a concave mirror and to determine the value of v for different values of u. |
| Apparatus Required | An optical bench with three uprights A concave mirror A mirror holder Two optical needles A knitting needle A half-meter scale |
| Theory | To find the value of v for different values of u in case of a concave mirror, we can use the mirror formula which relates the object distance (u), image distance (v), and focal length (f) of the mirror as follows: 1/f = 1/u + 1/v This formula can be rearranged to solve for v: 1/v = 1/f – 1/u v = 1/ (1/f – 1/u) Using this formula, we can calculate the value of v for different values of u, given the focal length of the concave mirror. To find the focal length of the concave mirror, we can use the formula: f = R/2 where R is the radius of curvature of the mirror. The radius of curvature is the distance between the center of curvature and the vertex of the mirror. Alternatively, we can use the mirror formula to find the focal length by placing an object at a known distance u from the mirror and measuring the distance v of the resulting image. Then we can rearrange the formula to solve for f: 1/f = 1/u + 1/v f = u*v / (u+v) Once we have determined the focal length, we can use the mirror formula to calculate the image distance for any given object distance. |
| Procedure | Set up the apparatus by placing the concave mirror on the stand, and the light source on the opposite side of the mirror. Place the screen or piece of paper at a distance from the mirror, so that it can capture the image formed by the mirror. Switch on the light source and adjust its position so that it is focused on the mirror. Place an object (such as a pencil or a coin) at a known distance u from the mirror. Adjust the position of the screen or paper until a clear and sharp image of the object is formed on it. Measure the distance v between the mirror and the image on the screen or paper. Repeat steps 4 to 6 for different values of u, ranging from near the focal point to infinity. Record the values of u and v for each measurement. |
| Observation and Result | Observation: As the object is moved closer to the mirror, the image distance v decreases. When the object is placed at the focal point of the mirror, the image distance becomes infinite. When the object is placed between the focal point and the mirror, the image distance becomes negative, indicating that the image is virtual and upright. As the object is moved further away from the mirror, the image distance increases. Result: The focal length of the concave mirror can be calculated using the formula f = u*v / (u+v), where u is the object distance and v is the image distance. The values of u and v for different measurements can be plotted on a graph, with u on the x-axis and v on the y-axis. The graph should show a curve that intersects the x-axis at the focal point of the mirror. The slope of the graph can also be used to determine the focal length of the mirror. |
