A : If a thin soap film is arranged vertically the spectrum of coloured fringes are spread equally on the film.
R : The colours of the film is dependent on the thickness of film and wavelength of the light.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To analyze the given statements A and R, we will evaluate each statement individually and then determine their relationship.

### Step 1: Analyze Statement A
Statement A claims that if a thin soap film is arranged vertically, the spectrum of colored fringes is spread equally on the film.

- **Explanation**: When light reflects off the surfaces of a thin soap film, it undergoes interference. The arrangement of the film (vertical or horizontal) does not affect the formation of colored fringes; rather, it is the thickness of the film and the wavelength of the light that influence the colors observed. Therefore, this statement is somewhat misleading as the arrangement alone does not guarantee equal spreading of colors.

### Step 2: Analyze Statement R
Statement R states that the colors of the film are dependent on the thickness of the film and the wavelength of the light.

- **Explanation**: This statement is accurate. The colors observed in a soap film arise from constructive and destructive interference of light waves reflecting off the top and bottom surfaces of the film. The thickness of the film determines the path difference between the reflected waves, and the wavelength of the light determines which colors will constructively interfere. Thus, the colors are indeed dependent on both the thickness of the film and the wavelength of the light.

### Step 3: Conclusion
Now, let's determine the relationship between statements A and R.

- **Conclusion**: Statement A is not entirely correct as it oversimplifies the conditions for the appearance of colored fringes. Statement R, however, is true and provides the correct reasoning behind the colors observed in a soap film. Therefore, A is false, and R is true.

### Final Answer
- A is false, and R is true.

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