The glass rod of Exercise 34.22 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod's axis is to be d 1.20 m inside the rod. How far from the left end of the rod must the object be located to form the image?

Verified step by step guidance

1. Identify the physical situation: A glass rod is immersed in oil, and an object is placed to the left of the rod on its axis. The goal is to find the position of the object such that its image forms 1.20 m inside the rod.
2. Recall that the image formation inside the rod depends on the refraction of light at the interface between the oil and the glass rod. The key concept here is the apparent depth or the refraction of light between two media with different refractive indices.
3. Use the relationship between real depth (d), apparent depth (d'), and refractive indices: \(d' = d \times \frac{n_2}{n_1}\), where \(n_1\) is the refractive index of the medium where the object is located (oil, \(n=1.45\)), and \(n_2\) is the refractive index of the rod (glass, which you should find from Exercise 34.22 or assume a typical value).
4. Set the apparent depth \(d'\) equal to 1.20 m (the image position inside the rod) and solve for the real distance \(d\) from the left end of the rod where the object must be placed.
5. Express the final formula for the object distance as \(d = d' \times \frac{n_1}{n_2}\), and substitute the known values to find the required object position relative to the left end of the rod.

Key Concepts

Refraction

Refraction is the bending of light as it passes from one medium to another with a different refractive index. This phenomenon occurs because light travels at different speeds in different materials. The degree of bending can be described by Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media.

Refractive Index

The refractive index (n) is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. A higher refractive index indicates that light travels slower in that medium. In this case, the oil has a refractive index of 1.45, which will affect how light behaves as it moves from the glass rod into the oil.

Optical Axis

The optical axis is an imaginary line that defines the path along which light travels through an optical system, such as a lens or a rod. In this scenario, the object is placed along the optical axis of the glass rod, which is crucial for determining the position where the light rays converge or diverge, ultimately affecting the image formation.