A glass hemisphere of radius `10 cm` and `mu=1.5` is silvered over its curved surface. There is an air bubble in the glass `5 cms` from the plane surface along the axis. Find the position of the images of this bubble seen by observer looking along the axis into the flat surface of the atmosphere.

Explanation

To solve the problem step by step, we will follow the principles of refraction and reflection.

### Step 1: Understanding the Setup
We have a glass hemisphere with a radius of 10 cm and a refractive index (μ) of 1.5. An air bubble is located 5 cm from the flat surface of the hemisphere along the axis. The curved surface is silvered, making it act as a mirror.

### Step 2: Finding the Apparent Depth of the Bubble
The apparent depth (h') of the bubble when viewed from the air (rarer medium) can be calculated using the formula:

\[ h' = \frac{h}{\mu} \]

Where:
- \( h \) = actual depth of the bubble = 5 cm
- \( \mu \) = refractive index of glass = 1.5

Substituting the values:

\[ h' = \frac{5 \text{ cm}}{1.5} = \frac{5 \times 2}{3} = \frac{10}{3} \approx 3.33 \text{ cm} \]

This means that the first image of the bubble, as seen by an observer looking into the flat surface, is located approximately 3.33 cm from the flat surface.

### Step 3: Finding the Focal Length of the Mirror
The radius of curvature (R) of the hemisphere is given as 10 cm. The focal length (f) of a spherical mirror is given by:

\[ f = \frac{R}{2} \]

Substituting the value:

\[ f = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \]

### Step 4: Locating the Object Relative to the Mirror
The bubble is located 5 cm from the flat surface, which is also the same distance from the silvered curved surface (mirror). Since the object (bubble) is at the focal point of the mirror (5 cm), we can analyze the image formation.

### Step 5: Image Formation by the Mirror
When the object is located at the focal point of a concave mirror, the image formed is at infinity. Thus, the second image of the bubble, as seen by the observer, is formed at infinity.

### Final Answer
1. The first image of the bubble is located at approximately **3.33 cm** from the flat surface.
2. The second image of the bubble is formed at **infinity**.