It is a problem similar to find out apparent depth.
Let the insect is at a point O. The rays OA and OB are starting from O and are refracted along AD and BC. Here AO is real depth = 3.8 cm and AI = apparent Depth = x. Using Snell's Law at point B
AS BI = AI and BO = AO because size of the pupil is very small the ray BC will enter in the eye if B is close to A.
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