A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths `f_(e)` and `f_(0)`, respectively. Then
`{:("Column I","Column II"),("(A)Intensity of light","(P)Radius of aperature R"),("received by lens",),("(B)Angular magnification","(Q) Dispersion of lens"),("(C) Length of telescope","(R) focal length "f_(0)"," f_(e)),("(D) Sharpness of image","(S) spherical aberration"):}`

Answer

To solve the problem, we need to match the items in Column I with the appropriate items in Column II based on the properties of a simple telescope. Let's go through each item step by step.

### Step 1: Intensity of light received by lens
- **Explanation**: The intensity of light received by the lens is related to the area of the lens. The area of the lens is proportional to the square of its radius (R). Therefore, the intensity of light is inversely proportional to the radius of the aperture (R).
- **Match**: (A) Intensity of light → (P) Radius of aperture R

### Step 2: Angular magnification
- **Explanation**: The angular magnification (M) of a telescope is given by the formula \( M = \frac{f_0}{f_e} \), where \( f_0 \) is the focal length of the objective lens and \( f_e \) is the focal length of the eyepiece. Thus, angular magnification depends on the focal lengths of the lenses.
- **Match**: (B) Angular magnification → (R) Focal lengths \( f_0 \) and \( f_e \)

### Step 3: Length of telescope
- **Explanation**: The length of the telescope (L) is the sum of the focal lengths of the objective and eyepiece lenses, given by \( L = f_0 + f_e \). Therefore, the length of the telescope is directly related to the focal lengths of the lenses.
- **Match**: (C) Length of telescope → (R) Focal lengths \( f_0 \) and \( f_e \)

### Step 4: Sharpness of image
- **Explanation**: The sharpness of the image depends on several factors, including the quality of the lens, the dispersion of light, and spherical aberration. It does not depend on the focal length of the lenses. Therefore, sharpness is influenced by the properties of the lens rather than its focal length.
- **Match**: (D) Sharpness of image → (S) Spherical aberration

### Final Matches:
- (A) Intensity of light → (P) Radius of aperture R
- (B) Angular magnification → (R) Focal lengths \( f_0 \) and \( f_e \)
- (C) Length of telescope → (R) Focal lengths \( f_0 \) and \( f_e \)
- (D) Sharpness of image → (S) Spherical aberration

### Summary of Matches:
1. (A) → (P)
2. (B) → (R)
3. (C) → (R)
4. (D) → (S)