A double convex lens has a focal length of 10 cm. If it is made of a material with a refractive index of 1.5, what is the radius of curvature of each surface assuming they are equal?
Practice Questions
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Q1
A double convex lens has a focal length of 10 cm. If it is made of a material with a refractive index of 1.5, what is the radius of curvature of each surface assuming they are equal?
15 cm
20 cm
25 cm
30 cm
Using the lens maker's formula, R = 2f(n-1) = 2*10*(1.5-1) = 20 cm.
Questions & Step-by-step Solutions
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Q
Q: A double convex lens has a focal length of 10 cm. If it is made of a material with a refractive index of 1.5, what is the radius of curvature of each surface assuming they are equal?
Solution: Using the lens maker's formula, R = 2f(n-1) = 2*10*(1.5-1) = 20 cm.
Steps: 7
Step 1: Understand the problem. We have a double convex lens with a focal length (f) of 10 cm and a refractive index (n) of 1.5.
Step 2: Recall the lens maker's formula, which is R = 2f(n - 1). This formula helps us find the radius of curvature (R) of the lens surfaces.
Step 3: Substitute the values into the formula. We have f = 10 cm and n = 1.5.
Step 4: Calculate (n - 1). This is 1.5 - 1 = 0.5.
Step 5: Multiply f by 2 and then by (n - 1). This gives us 2 * 10 * 0.5.
Step 6: Perform the multiplication. 2 * 10 = 20, and then 20 * 0.5 = 10.
Step 7: Therefore, R = 10 cm. This is the radius of curvature for each surface of the lens.
