Question

The sun is 1.5×10¹¹m from earth; its diameter is 1.4×10⁹m. A hiker who wishes to start a fire uses a 6.0-cm-diameter lens with a focal length of 12 cm to focus the sun's rays onto a piece of wood. What is the distance between the lens and the piece of wood?

1) 10 cm
2) 20 cm
3) 30 cm
4) 40 cm

Answer 1

The distance between the lens and the piece of wood is approximately 12 cm. So, the correct option is 1) 10 cm.

Step-by-step explanation:

To find the distance between the lens and the piece of wood, we can use the lens formula: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance. Since the lens is being used to focus the sun's rays onto the wood, the object distance (u) is the distance between the lens and the sun, which is 1.5×10¹¹m. The focal length of the lens is given as 12 cm (0.12 m). We need to find the image distance (v).

Using the lens formula, we can rearrange it to solve for v: v = 1 / (1/f + 1/u). Substitute the values into the equation: v = 1 / (1/0.12 + 1/1.5×10¹¹).

After calculating, the value of v is approximately 0.120000000000012 m. Therefore, the distance between the lens and the piece of wood is approximately 0.120000000000012 m, which is equivalent to 12 cm. So, the correct option is 1) 10 cm.