Image on the left shows a cylinder kept on the top of a cube. Height of the cylinder and side of the cube are equal. Parallel rays of light are falling on them at an angle of 45 degree. Which option shows the correct shadow?
Show Hint
With light at 45 degrees, the shadow length of a vertical feature is equal to its height. Remember that the shadow of a cylinder cast by parallel light ends in a semicircle, not a straight line.
Step 1: Understanding the Concept:
This is a problem about shadow projection. We need to determine the shape of the shadow cast on a planar surface by a composite 3D object (a cylinder on a cube) when illuminated by parallel light rays at a 45-degree angle.
Step 2: Key Formula or Approach:
The length of the shadow cast by a vertical object of height \(h\) with light at a 45-degree angle is also \(h\). We need to calculate the shadow for each part of the object and combine them.
1. Calculate the shadow of the cube.
2. Calculate the shadow of the cylinder, noting that it starts from the top of the cube.
3. Combine the projected shadows on the ground plane.
Step 3: Detailed Explanation:
Let the side of the cube be \(L\). The height of the cylinder is also \(L\).
Shadow of the Cube: The cube has a height of \(L\). The light at 45 degrees will cast a shadow of the cube's vertical form onto the ground. This shadow will be a square of side \(L\), directly adjacent to the cube's base.
Shadow of the Cylinder: The cylinder also has a height of \(L\). Its shadow will extend a horizontal distance of \(L\) from its base.
Combined Shadow: The cylinder sits on top of the cube. Therefore, the shadow of the cylinder begins where the shadow of the cube ends.
The total length of the shadow from the base of the cube will be: (Length of cube's shadow) + (Length of cylinder's shadow) = \(L + L = 2L\).
The width of the shadow will be determined by the widest part, which is the cube (width \(L\)). The cylinder is narrower.
The shape of the shadow's end is determined by the object casting the furthest part of the shadow, which is the cylinder. The shadow of a cylinder's curved side and circular top cast by parallel light is a rectangle with a semicircular end.
So, the final shadow should be composed of a square of side \(L\) (from the cube) seamlessly joined to a rectangle (from the cylinder's side) of length \(L\) and width equal to the cylinder's diameter, capped by a semicircle.
Let's check the options:
(A) Incorrectly shows the shadows as separate.
(B) Shows the cylinder's shadow as shorter than the cube's shadow. This is incorrect as both objects have the same height \(L\), and thus cast shadows of the same length \(L\).
(C) This correctly shows a square shadow for the cube attached to a rectangular shadow for the cylinder, which ends in a semicircle. The length of the cylinder's shadow part is equal to the length of the cube's shadow part. This is the correct representation.
(D) This shows the end of the shadow as a straight line, which is incorrect. The shadow of the cylinder must have a rounded end.
Step 4: Final Answer:
Option (C) correctly depicts the combined shadow, showing the correct relative lengths and the characteristic semicircular end of the cylinder's shadow.
