Question

When a body of refractive index \( \mu = 1.4 \) is put into a liquid, the body becomes invisible. What would be the refractive index of the medium?

• A. \( \mu = 1 \)
• B. \( \mu = 0.7 \)
• C. \( \mu = 2.4 \)
• D. \( \mu = 1.4 \)

Hint:

An object becomes invisible in a medium when both have the same refractive index, because there is no significant refraction at the boundary.

Answer 1

The Correct Option is D

Step 1: Understand the condition of invisibility.
A body becomes invisible in a liquid when light does not bend or reflect noticeably at the boundary between the body and the liquid.

Step 2: Relate invisibility with refractive index.
This happens when the refractive index of the body is equal to the refractive index of the surrounding medium.

Step 3: Write the given refractive index of the body.
The refractive index of the body is given as:
\[ \mu_{\text{body}} = 1.4 \]

Step 4: Apply the invisibility condition.
For the body to become invisible:
\[ \mu_{\text{medium}} = \mu_{\text{body}} \]

Step 5: Substitute the value.
\[ \mu_{\text{medium}} = 1.4 \]

Step 6: Match with the options.
The value \( \mu = 1.4 \) is given in option (D).

Step 7: Final Answer.
Therefore, the refractive index of the medium is:
\[ \boxed{\mu = 1.4} \]