A double convex lens has a focal length of 10 cm. If it is made of a material wi
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Lens Maker's Formula – The formula relates the focal length of a lens to the radii of curvature of its surfaces and the refractive index of the material.
Refractive Index – A measure of how much light bends when entering a material, affecting the lens's focal length.
Focal Length – The distance from the lens where parallel rays of light converge, determined by the lens's shape and material.
