Okay, let's tackle this question about diplopia when looking up and out. The patient's symptom is diplopia in that specific direction, so I need to figure out which extraocular muscle is involved.

First, I remember that the extraocular muscles control eye movements. There are six muscles: four rectus muscles (superior, inferior, medial, lateral) and two oblique muscles (superior and inferior). Each muscle has a specific action, and certain muscles work together for combined movements like up and out.

When the eye is looking up and out, the primary muscles involved would be the superior rectus and the inferior oblique. The superior rectus is mainly for elevation, but it also helps in adduction. However, when the eye is abducted (looking out), the inferior oblique becomes more active. The inferior oblique is responsible for elevation, abduction, and extorsion. So if the eye is looking up and out, the inferior oblique is likely the main muscle involved.

Wait, but the superior rectus also contributes to elevation. But in the position of adduction, the superior rectus acts more as a depressor. Hmm, maybe I'm mixing up the actions. Let me think again. The inferior oblique is active in abduction, elevation, and extorsion. So when the eye is looking up and out, the inferior oblique would be the main muscle. If that's paralyzed or defective, the patient can't perform that movement, leading to diplopia.

The options were A-D, but the correct answer is the inferior oblique. Let me check why other options are wrong. The superior oblique is involved in depression and intorsion, so if it's defective, maybe the problem is down and in. The lateral rectus is for abduction, but not elevation. The medial rectus is for adduction. So the most likely defective muscle here is the inferior oblique.

**Core Concept**
Diplopia (double vision) in specific gaze directions relates to dysfunction of extraocular muscles responsible for coordinated eye movements. The **inferior oblique muscle** is critical for elevation and abduction, particularly when the eye is in an abducted position.

**Why the Correct Answer is Right**
The inferior oblique muscle elevates the eye when it is abducted (looking "up and out") and also contributes to abduction and extorsion. Damage or paralysis of this muscle (e.g., from trauma or palsy) impairs the ability to perform this combined movement, leading to diplopia in that direction. Its action is most prominent in the abducted position due to the oblique’s orientation and synergistic interactions with other muscles.

**Why Each Wrong Option is Incorrect**
**Option A:** The superior rectus primarily elevates the eye in adduction and does not play a significant role in abduction.
**Option B:** The superior oblique depresses the eye in abduction and causes intorsion, not elevation.
**Option C:** The lateral rectus abducts the eye but does not elevate it.

**Clinical Pearl / High-Yield Fact**
Remember the **"up and out"** rule: Inferior oblique palsy causes diplopia when the affected eye tries to look upward and outward. This is a classic clinical finding in isolated inferior oblique dysfunction.

**Correct Answer: C. Inferior oblique**

✓ Correct Answer: A. Right Superior rectus