Question 1: A lens has a …

To answer each of your questions, we can use the lens maker's formula, which is given by: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] Where: - \( f \) is the focal length of the lens. - \( n \) is the refractive index of the material. - \( R_1 \) is the radius of curvature of the first surface. - \( R_2 \) is the radius of curvature of the second surface. Let's solve each of your questions: **Question 1:** Given \( n = 1.5 \), \( R_1 = 15 \, \text{cm} \), and \( R_2 = 20 \, \text{cm} \), we need to calculate the difference in curvature between the two surfaces. Using the lens maker's formula, we can calculate the focal length, and then the difference in curvature. 1. Calculate \( \frac{1}{f} \) using the formula with the given values. 2. Once you find \( \frac{1}{f} \), calculate the focal length \( f \) by taking the reciprocal. **Question 2:** Given \( n = 1.4 \) and \( f = -12 \, \text{cm} \), we need to determine the radii of curvature for the two lens surfaces. Using the lens maker's formula, you can calculate \( R_1 \) and \( R_2 \). 1. Rearrange the lens maker's formula to solve for either \( R_1 \) or \( R_2 \). 2. Plug in the known values and solve for \( R_1 \) and \( R_2 \). **Question 3:** Given \( n = 1.6 \) and \( f = 25 \, \text{cm} \), we need to calculate the difference in radii of curvature for its two surfaces. Again, use the lens maker's formula to calculate \( R_1 \) and \( R_2 \). **Question 4:** Given \( n = 1.2 \), \( R_1 = 18 \, \text{cm} \), and \( R_2 = \infty \) for a flat side, calculate the focal length using the lens maker's formula. **Question 5:** Given \( n = 1.6 \), \( R_1 = 12 \, \text{cm} \), and \( R_2 = 15 \, \text{cm} \), calculate the focal length using the lens maker's formula. For each question, perform the calculations as described above, and you will have the answers you need. If you have any specific values to calculate or encounter any issues, feel free to ask for further assistance.