| Aim | Determining the Radius of Curvature of a Spherical Surface using a Spherometer |
| Apparatus Required | Spherical surface Spherometer Meter ruler Calculator Paper and pencil for recording measurements |
| Theory | A spherometer is an instrument that is used to measure the radius of curvature of a spherical surface. It works by measuring the distance between the three legs of the spherometer when placed on the surface. In this experiment, we will use a spherometer to determine the radius of curvature of a given spherical surface. The least count of a spherometer is determined by the smallest measurement that can be taken on the Vernier scale. Typically, the main scale of a spherometer is divided into increments of 0.1 mm or 0.01 mm. The Vernier scale is divided into a number of divisions that correspond to a fraction of the main scale division, usually 25 or 50 divisions. To determine the least count of the spherometer, we need to find the smallest measurement that can be taken on the Vernier scale. This is calculated by dividing the main scale reading by the number of divisions on the Vernier scale. For example, if the main scale reading is 3.0 mm and there are 50 divisions on the Vernier scale, the least count of the spherometer would be: 0.1 mm / 50 = 0.002 mm Therefore, the least count of the spherometer in this case is 0.002 mm. This means that the spherometer can measure changes in the radius of curvature of a spherical surface to a precision of 0.002 mm. |
| Procedure | Set up the spherometer on a flat surface. Adjust the three legs of the spherometer so that they are approximately equidistant from each other. Place the spherical surface on the flat surface, and position the spherometer on top of the surface with the three legs touching the surface. Record the reading on the main scale of the spherometer. Record the reading on the Vernier scale of the spherometer by aligning the lines on the Vernier scale with the lines on the main scale. Repeat steps 3-5 at different positions on the spherical surface to obtain multiple readings. Calculate the average reading of the spherometer. Measure the distance between two opposite legs of the spherometer using a meter ruler. Calculate the radius of curvature of the spherical surface using the formula: Radius of curvature = (Distance between two opposite legs)^2 / (8 x Average spherometer reading) |
| Observation and Results | Results: Record the measurements and calculations in a table. Calculate the average spherometer reading and the radius of curvature of the spherical surface. Discussion: Compare the calculated radius of curvature to the actual value (if known). Discuss the sources of error in the experiment and suggest ways to improve the accuracy of the measurements. Conclusion: In this experiment, we successfully used a spherometer to determine the radius of curvature of a given spherical surface. By taking multiple readings and calculating the average, we obtained a more accurate measurement of the radius of curvature. |
