diff --git a/out.jpg b/out.jpg
index 609e5c6..1e85428 100644
Binary files a/out.jpg and b/out.jpg differ
diff --git a/tinyraytracer.cpp b/tinyraytracer.cpp
index f2994a0..5e5806d 100644
--- a/tinyraytracer.cpp
+++ b/tinyraytracer.cpp
@@ -12,9 +12,10 @@ struct Light {
 };
 
 struct Material {
-    Material(const Vec3f &a, const Vec3f &color, const float &spec) : albedo(a), diffuse_color(color), specular_exponent(spec) {}
-    Material() : albedo(1,0,0), diffuse_color(), specular_exponent() {}
-    Vec3f albedo;
+    Material(const float &r, const Vec4f &a, const Vec3f &color, const float &spec) : refractive_index(r), albedo(a), diffuse_color(color), specular_exponent(spec) {}
+    Material() : refractive_index(1), albedo(1,0,0,0), diffuse_color(), specular_exponent() {}
+    float refractive_index;
+    Vec4f albedo;
     Vec3f diffuse_color;
     float specular_exponent;
 };
@@ -44,6 +45,19 @@ Vec3f reflect(const Vec3f &I, const Vec3f &N) {
     return I - N*2.f*(I*N);
 }
 
+Vec3f refract(const Vec3f &I, const Vec3f &N, const float &refractive_index) { // Snell's law
+    float cosi = - std::max(-1.f, std::min(1.f, I*N));
+    float etai = 1, etat = refractive_index;
+    Vec3f n = N;
+    if (cosi < 0) { // if the ray is inside the object, swap the indices and invert the normal to get the correct result
+        cosi = -cosi;
+        std::swap(etai, etat); n = -N;
+    }
+    float eta = etai / etat;
+    float k = 1 - eta*eta*(1 - cosi*cosi);
+    return k < 0 ? Vec3f(0,0,0) : I*eta + n*(eta * cosi - sqrtf(k));
+}
+
 bool scene_intersect(const Vec3f &orig, const Vec3f &dir, const std::vector<Sphere> &spheres, Vec3f &hit, Vec3f &N, Material &material) {
     float spheres_dist = std::numeric_limits<float>::max();
     for (size_t i=0; i < spheres.size(); i++) {
@@ -67,8 +81,11 @@ Vec3f cast_ray(const Vec3f &orig, const Vec3f &dir, const std::vector<Sphere> &s
     }
 
     Vec3f reflect_dir = reflect(dir, N).normalize();
+    Vec3f refract_dir = refract(dir, N, material.refractive_index).normalize();
     Vec3f reflect_orig = reflect_dir*N < 0 ? point - N*1e-3 : point + N*1e-3; // offset the original point to avoid occlusion by the object itself
+    Vec3f refract_orig = refract_dir*N < 0 ? point - N*1e-3 : point + N*1e-3;
     Vec3f reflect_color = cast_ray(reflect_orig, reflect_dir, spheres, lights, depth + 1);
+    Vec3f refract_color = cast_ray(refract_orig, refract_dir, spheres, lights, depth + 1);
 
     float diffuse_light_intensity = 0, specular_light_intensity = 0;
     for (size_t i=0; i<lights.size(); i++) {
@@ -84,7 +101,7 @@ Vec3f cast_ray(const Vec3f &orig, const Vec3f &dir, const std::vector<Sphere> &s
         diffuse_light_intensity  += lights[i].intensity * std::max(0.f, light_dir*N);
         specular_light_intensity += powf(std::max(0.f, -reflect(-light_dir, N)*dir), material.specular_exponent)*lights[i].intensity;
     }
-    return material.diffuse_color * diffuse_light_intensity * material.albedo[0] + Vec3f(1., 1., 1.)*specular_light_intensity * material.albedo[1] + reflect_color*material.albedo[2];
+    return material.diffuse_color * diffuse_light_intensity * material.albedo[0] + Vec3f(1., 1., 1.)*specular_light_intensity * material.albedo[1] + reflect_color*material.albedo[2] + refract_color*material.albedo[3];
 }
 
 void render(const std::vector<Sphere> &spheres, const std::vector<Light> &lights) {
@@ -118,13 +135,14 @@ void render(const std::vector<Sphere> &spheres, const std::vector<Light> &lights
 }
 
 int main() {
-    Material      ivory(Vec3f(0.6,  0.3, 0.1), Vec3f(0.4, 0.4, 0.3),   50.);
-    Material red_rubber(Vec3f(0.9,  0.1, 0.0), Vec3f(0.3, 0.1, 0.1),   10.);
-    Material     mirror(Vec3f(0.0, 10.0, 0.8), Vec3f(1.0, 1.0, 1.0), 1425.);
+    Material      ivory(1.0, Vec4f(0.6,  0.3, 0.1, 0.0), Vec3f(0.4, 0.4, 0.3),   50.);
+    Material      glass(1.5, Vec4f(0.0,  0.5, 0.1, 0.8), Vec3f(0.6, 0.7, 0.8),  125.);
+    Material red_rubber(1.0, Vec4f(0.9,  0.1, 0.0, 0.0), Vec3f(0.3, 0.1, 0.1),   10.);
+    Material     mirror(1.0, Vec4f(0.0, 10.0, 0.8, 0.0), Vec3f(1.0, 1.0, 1.0), 1425.);
 
     std::vector<Sphere> spheres;
     spheres.push_back(Sphere(Vec3f(-3,    0,   -16), 2,      ivory));
-    spheres.push_back(Sphere(Vec3f(-1.0, -1.5, -12), 2,      mirror));
+    spheres.push_back(Sphere(Vec3f(-1.0, -1.5, -12), 2,      glass));
     spheres.push_back(Sphere(Vec3f( 1.5, -0.5, -18), 3, red_rubber));
     spheres.push_back(Sphere(Vec3f( 7,    5,   -18), 4,     mirror));