Explanation:
When the smallest division of a vernier is longer than the smallest division of its primary scale, the vernier is known as a retrograde vernier. Let's understand the concept of a retrograde vernier in detail.

Vernier Scale:
A vernier scale is a measuring instrument used to read fractional measurements more accurately than a regular scale. It consists of a primary scale and a sliding secondary scale called the vernier scale. The primary scale is divided into equal divisions, while the vernier scale has a slightly longer length and is divided into a smaller number of divisions.

Retrograde Vernier:
A retrograde vernier is a type of vernier scale where the smallest division of the vernier scale is longer than the smallest division of the primary scale. In other words, the length of each division on the vernier scale is greater than the length of each division on the primary scale.

Working Principle:
In a retrograde vernier, the zero point of the vernier scale is located to the left of the zero point of the primary scale. As the vernier scale is moved to the right, the divisions on the vernier scale align with the divisions on the primary scale. However, due to the longer length of each division on the vernier scale, the alignment occurs at a point where the divisions on the vernier scale are not aligned with the divisions on the primary scale.

Reading Measurements:
To read a measurement using a retrograde vernier, follow these steps:
1. Align the zero point of the vernier scale with a reference point on the primary scale.
2. Look for the first division on the vernier scale that aligns with a division on the primary scale.
3. Determine the fractional measurement by counting the number of divisions on the primary scale before the aligned division.
4. Read the fractional measurement from the vernier scale by identifying the division that aligns with the reference point on the primary scale.
5. Add the fractional measurement from the vernier scale to the measurement obtained from the primary scale to get the final measurement.

Advantages:
The retrograde vernier allows for more accurate measurements compared to a regular vernier scale. It provides finer divisions and allows for measurements with greater precision. However, it requires a bit more skill and practice to read measurements accurately due to the alignment of divisions occurring at a non-zero point on the vernier scale.

Therefore, the correct answer is option C) Retrograde vernier.