A student is getting her picture taken by a digital camera. The student is h₀= 1.55 m tall and she stands do m in front of the camera lens which has a focal length of f = 0.017 m. Input an expression for the resulting image distance, dᵢ.

The expression for the resulting image distance, dᵢ, when a student of height h₀ = 1.55 m stands d₀ meters in front of a digital camera with a focal length of f = 0.017 m, is dᵢ = 1 / ((1/f) - (1/d₀)).

In optics, the lens equation relates the object distance (d₀), the image distance (dᵢ), and the focal length of the lens (f) through the equation 1/f = 1/d₀ + 1/dᵢ. Rearranging this equation, we get dᵢ = 1 / ((1/f) - (1/d₀)), which gives us the image distance.

Given that the student's height is h₀ = 1.55 m, and she stands d₀ meters in front of the camera, we can use this expression to calculate the resulting image distance.

This formula is essential for understanding how objects are imaged by lenses in cameras, enabling precise positioning of subjects to achieve desired photographic outcomes.