diff --git a/ray-tracer/src/types/mod.rs b/ray-tracer/src/types/mod.rs
index e2a03b0..34bc3c6 100644
--- a/ray-tracer/src/types/mod.rs
+++ b/ray-tracer/src/types/mod.rs
@@ -156,4 +156,18 @@ mod tests {
         *c.pixel_mut(2, 3) = red;
         assert_eq!(*c.pixel(2, 3), red);
     }
+
+    #[test]
+    fn reflect_vector_approaching_at_45() {
+        let v = Vector::new(1., -1., 0.);
+        let n = Vector::new(0., 1., 0.);
+        assert_eq!(v.reflect(&n), Vector::new(1., 1., 0.));
+    }
+
+    #[test]
+    fn reflect_off_slanted_surface() {
+        let v = Vector::new(0., -1., 0.);
+        let n = Vector::new(2_f64.sqrt() / 2., 2_f64.sqrt() / 2., 0.);
+        assert_eq!(v.reflect(&n), Vector::new(1., 0., 0.));
+    }
 }
diff --git a/ray-tracer/src/types/vector.rs b/ray-tracer/src/types/vector.rs
index eb0f8bb..3c8f88d 100644
--- a/ray-tracer/src/types/vector.rs
+++ b/ray-tracer/src/types/vector.rs
@@ -42,6 +42,10 @@ impl Vector {
         let z = self.x() * r.y() - self.y() * r.x();
         Self::new(x, y, z)
     }
+
+    pub fn reflect(&self, n: &Vector) -> Self {
+        self - (n * 2. * self.dot(n))
+    }
 }
 
 impl Default for Vector {
@@ -66,15 +70,36 @@ impl std::ops::Deref for Vector {
 
 impl std::ops::Add for Vector {
     type Output = Vector;
-    fn add(self, r: Self) -> Self {
+    fn add(self, r: Self) -> Self::Output {
         Vector::from(self.0 + r.0)
     }
 }
 
+impl std::ops::Sub<&Vector> for &Vector {
+    type Output = Vector;
+    fn sub(self, r: &Vector) -> Self::Output {
+        Vector::from(self.0 - r.0)
+    }
+}
+
+impl std::ops::Sub<Vector> for &Vector {
+    type Output = Vector;
+    fn sub(self, r: Vector) -> Self::Output {
+        self - &r
+    }
+}
+
+impl std::ops::Sub<&Vector> for Vector {
+    type Output = Vector;
+    fn sub(self, r: &Vector) -> Self::Output {
+        &self - r
+    }
+}
+
 impl std::ops::Sub for Vector {
     type Output = Vector;
-    fn sub(self, r: Self) -> Self {
-        Vector::from(self.0 - r.0)
+    fn sub(self, r: Vector) -> Self::Output {
+        &self - &r
     }
 }
 
@@ -87,6 +112,13 @@ impl std::ops::Neg for Vector {
     }
 }
 
+impl std::ops::Mul<f64> for &Vector {
+    type Output = Vector;
+    fn mul(self, r: f64) -> Self::Output {
+        Vector::from(self.0 * r)
+    }
+}
+
 impl std::ops::Mul<f64> for Vector {
     type Output = Vector;
     fn mul(self, r: f64) -> Self {