Question

Make the curvature radius 0.6 m, the refractive index 1.5, and the diameter 0.6 m. place the lamp so that the source of light is 120 cm from the middle of the lens (use the ruler). the focal length of the lens is ____________, and the focal plane is ___________ from the lens.

Answer 1

To find the focal length of the lens, the Lens Maker's Equation can be used. With the given information, we can calculate the focal length to be approximately 1.2 m. The focal plane is also located at a distance equal to the focal length of the lens.

Step-by-step explanation:

To calculate the focal length of a lens, we can use the Lens Maker's Equation. The equation is given by:

1/f = (n - 1) * (1/R₁ - 1/R₂)

where f is the focal length, n is the refractive index, R₁ is the radius of curvature of the first surface, and R₂ is the radius of curvature of the second surface. In this case, the lens is plano-convex, which means one surface is flat and the other is curved. Let's assume the flat surface is the first surface and has a radius of curvature of infinity. The second surface has a radius of curvature of -0.6 m. With a refractive index of 1.5, we can plug in these values into the equation to find the focal length:

1/f = (1.5 - 1) * (1/infinity - 1/-0.6)

Since the radius of curvature of the first surface is infinity, the first term becomes zero. Simplifying the equation further, we get:

1/f = (1.5 - 1) * (0 + 1.67)

1/f = 0.5 * 1.67

1/f = 0.835

Solving for f, we find:

f = 1/0.835

f ≈ 1.2 m

The focal plane is located at a distance equal to the focal length of the lens. Therefore, the focal plane is approximately 1.2 m from the lens.

Answer 2

We are given
r = 0.6 m
n = 1.5
D = 0.6 m, R1 = 30 cm
R2 = 120 cm

We are asked to get the focal length and the distance of the focal plane from the lens

We use the formula
1 / f = ( n - 1) (1/R1 - 1/R2)
Substituting and solving for f
1/ f = (1.5 - 1) (1/30 - 1/120)
f = 80 cm

The focal length is 80 cm and the distance of the focal plane from the lesn is 80 cm - 30 cm = 50 cm.