To find the ratio of the number of students going on the field trip to the number of students staying at school, we first need to determine how many students are staying at school.
The total number of students is 41, and the number of students going on the field trip is 13. Therefore, the number of students staying at school is:
\[ 41 - 13 = 28 \]
Now, we can set up the ratio of students going on the field trip to students staying at school:
\[ \text{Ratio} = \frac{\text{Students going on field trip}}{\text{Students staying at school}} = \frac{13}{28} \]
This ratio can be simplified if necessary. However, since 13 and 28 have no common factors (13 is a prime number), the ratio \( \frac{13}{28} \) is already in its simplest form.
Thus, the final answer is:
\[ \text{The ratio is } 13:28. \]